├── .gitignore ├── Double_Finite_Square_Well.ipynb ├── Finite Well Bound States.ipynb ├── Harmonic Oscillator.ipynb ├── Homework3_plucked_string.ipynb ├── Homework_1_problem1.2.ipynb ├── Homework_1_problem2.2.ipynb ├── Infinite_Square_Well_Solutions.ipynb ├── Linear Potential in QM.ipynb ├── ODE_with_Python.ipynb ├── Plots.ipynb ├── README.md ├── Solving_the_Schrodinger_Equation_Numerically.ipynb └── TimePropagation_of_WF.ipynb /.gitignore: -------------------------------------------------------------------------------- 1 | ## Core latex/pdflatex auxiliary files: 2 | *.aux 3 | *.lof 4 | *.log 5 | *.lot 6 | *.fls 7 | *.out 8 | *.toc 9 | *.fmt 10 | *.fot 11 | *.cb 12 | *.cb2 13 | 14 | ## Intermediate documents: 15 | *.dvi 16 | *-converted-to.* 17 | # these rules might exclude image files for figures etc. 18 | # *.ps 19 | # *.eps 20 | # *.pdf 21 | 22 | ## Generated if empty string is given at "Please type another file name for output:" 23 | .pdf 24 | 25 | ## Bibliography auxiliary files (bibtex/biblatex/biber): 26 | *.bbl 27 | *.bcf 28 | *.blg 29 | *-blx.aux 30 | *-blx.bib 31 | *.run.xml 32 | 33 | ## Build tool auxiliary files: 34 | *.fdb_latexmk 35 | *.synctex 36 | *.synctex(busy) 37 | *.synctex.gz 38 | *.synctex.gz(busy) 39 | *.pdfsync 40 | 41 | ## Auxiliary and intermediate files from other packages: 42 | # algorithms 43 | *.alg 44 | *.loa 45 | 46 | # achemso 47 | acs-*.bib 48 | 49 | # amsthm 50 | *.thm 51 | 52 | # beamer 53 | *.nav 54 | *.pre 55 | *.snm 56 | *.vrb 57 | 58 | # changes 59 | *.soc 60 | 61 | # cprotect 62 | *.cpt 63 | 64 | # elsarticle (documentclass of Elsevier journals) 65 | *.spl 66 | 67 | # endnotes 68 | *.ent 69 | 70 | # fixme 71 | *.lox 72 | 73 | # feynmf/feynmp 74 | *.mf 75 | *.mp 76 | *.t[1-9] 77 | *.t[1-9][0-9] 78 | *.tfm 79 | 80 | #(r)(e)ledmac/(r)(e)ledpar 81 | *.end 82 | *.?end 83 | *.[1-9] 84 | *.[1-9][0-9] 85 | *.[1-9][0-9][0-9] 86 | *.[1-9]R 87 | *.[1-9][0-9]R 88 | *.[1-9][0-9][0-9]R 89 | *.eledsec[1-9] 90 | *.eledsec[1-9]R 91 | *.eledsec[1-9][0-9] 92 | *.eledsec[1-9][0-9]R 93 | *.eledsec[1-9][0-9][0-9] 94 | *.eledsec[1-9][0-9][0-9]R 95 | 96 | # glossaries 97 | *.acn 98 | *.acr 99 | *.glg 100 | *.glo 101 | *.gls 102 | *.glsdefs 103 | 104 | # gnuplottex 105 | *-gnuplottex-* 106 | 107 | # gregoriotex 108 | *.gaux 109 | *.gtex 110 | 111 | # hyperref 112 | *.brf 113 | 114 | # knitr 115 | *-concordance.tex 116 | # TODO Comment the next line if you want to keep your tikz graphics files 117 | *.tikz 118 | *-tikzDictionary 119 | 120 | # listings 121 | *.lol 122 | 123 | # makeidx 124 | *.idx 125 | *.ilg 126 | *.ind 127 | *.ist 128 | 129 | # minitoc 130 | *.maf 131 | *.mlf 132 | *.mlt 133 | *.mtc[0-9]* 134 | *.slf[0-9]* 135 | *.slt[0-9]* 136 | *.stc[0-9]* 137 | 138 | # minted 139 | _minted* 140 | *.pyg 141 | 142 | # morewrites 143 | *.mw 144 | 145 | # nomencl 146 | *.nlo 147 | 148 | # pax 149 | *.pax 150 | 151 | # pdfpcnotes 152 | *.pdfpc 153 | 154 | # sagetex 155 | *.sagetex.sage 156 | *.sagetex.py 157 | *.sagetex.scmd 158 | 159 | # scrwfile 160 | *.wrt 161 | 162 | # sympy 163 | *.sout 164 | *.sympy 165 | sympy-plots-for-*.tex/ 166 | 167 | # pdfcomment 168 | *.upa 169 | *.upb 170 | 171 | # pythontex 172 | *.pytxcode 173 | pythontex-files-*/ 174 | 175 | # thmtools 176 | *.loe 177 | 178 | # TikZ & PGF 179 | *.dpth 180 | *.md5 181 | *.auxlock 182 | 183 | # todonotes 184 | *.tdo 185 | 186 | # easy-todo 187 | *.lod 188 | 189 | # xindy 190 | *.xdy 191 | 192 | # xypic precompiled matrices 193 | *.xyc 194 | 195 | # endfloat 196 | *.ttt 197 | *.fff 198 | 199 | # Latexian 200 | TSWLatexianTemp* 201 | 202 | ## Editors: 203 | # WinEdt 204 | *.bak 205 | *.sav 206 | 207 | # Texpad 208 | .texpadtmp 209 | 210 | # Kile 211 | *.backup 212 | 213 | # KBibTeX 214 | *~[0-9]* 215 | 216 | # auto folder when using emacs and auctex 217 | /auto/* 218 | 219 | # expex forward references with \gathertags 220 | *-tags.tex 221 | -------------------------------------------------------------------------------- /Finite Well Bound States.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "markdown", 5 | "metadata": {}, 6 | "source": [ 7 | "# Finite Square Well Bound State\n", 8 | "This notebook uses the technique from the Solving the Schrödinger Equation notebook to calculate the bound states for a finite square well. There are only a few changes to the square well solution. The potential is different, in that it has a small area which is not zero but some negative value, here $-V_0$. For our calculation to be approximately correct, we need to make sure that our entire calculation space, from $-a/2$ to $a/2$ is much larger than the well, wich is from $-b/2.$ to $b/2$. The factor 100 I choose here is probably more than needed. We also need a fairly large $N$, the number of steps in our space, so that the resulting wave function is smooth in the area of the well. You may need to be somewhat patient when evaluating the well with these settings!" 9 | ] 10 | }, 11 | { 12 | "cell_type": "code", 13 | "execution_count": 1, 14 | "metadata": {}, 15 | "outputs": [], 16 | "source": [ 17 | "import numpy as np\n", 18 | "import matplotlib.pyplot as plt\n", 19 | "import scipy.linalg as scl\n", 20 | "hbar=1\n", 21 | "m=1\n", 22 | "N = 4097\n", 23 | "a = 200.0\n", 24 | "b = 2.\n", 25 | "x = np.linspace(-a/2.,a/2.,N)\n", 26 | "# We want to store step size, this is the reliable way:\n", 27 | "h = x[1]-x[0] # Should be equal to 2*np.pi/(N-1)\n", 28 | "V0 = -6.\n", 29 | "V=np.zeros(N)\n", 30 | "for i in range(N):\n", 31 | " if x[i]> -b/2. and x[i]< b/2.:\n", 32 | " V[i]= V0\n", 33 | "\n", 34 | "Mdd = 1./(h*h)*(np.diag(np.ones(N-1),-1) -2* np.diag(np.ones(N),0) + np.diag(np.ones(N-1),1))\n", 35 | "H = -(hbar*hbar)/(2.0*m)*Mdd + np.diag(V) \n", 36 | "E,psiT = np.linalg.eigh(H) # This computes the eigen values and eigenvectors\n", 37 | "psi = np.transpose(psiT) # We take the transpose of psiT to the wavefunction vectors can accessed as psi[n]\n", 38 | "#" 39 | ] 40 | }, 41 | { 42 | "cell_type": "code", 43 | "execution_count": 2, 44 | "metadata": {}, 45 | "outputs": [ 46 | { 47 | "data": { 48 | "image/png": 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\n", 49 | "text/plain": [ 50 | "
" 51 | ] 52 | }, 53 | "metadata": { 54 | "needs_background": "light" 55 | }, 56 | "output_type": "display_data" 57 | } 58 | ], 59 | "source": [ 60 | "plt.figure(figsize=(10,7))\n", 61 | "plt.xlim((-5*b,5*b))\n", 62 | "plt.plot(x,V/(-V0),color=\"Gray\",label=\"V(x) scaled to 1\")\n", 63 | "for i in range(5):\n", 64 | " if E[i]<0: # Only plot the bound states. The scattering states are not reliably computed.\n", 65 | " if psi[i][N-10] < 0: # Flip the wavefunctions if it is negative at large x, so plots are more consistent.\n", 66 | " plt.plot(x,-psi[i]/np.sqrt(h),label=\"$E_{}$={:>8.3f}\".format(i,E[i]))\n", 67 | " else:\n", 68 | " plt.plot(x,psi[i]/np.sqrt(h),label=\"$E_{}$={:>8.3f}\".format(i,E[i]))\n", 69 | "plt.title(\"Solutions to the Finite Square Well\")\n", 70 | "plt.legend()\n", 71 | "plt.savefig(\"Finite_Square_Well_WaveFunctions.pdf\")\n", 72 | "plt.show()\n" 73 | ] 74 | }, 75 | { 76 | "cell_type": "code", 77 | "execution_count": null, 78 | "metadata": {}, 79 | "outputs": [], 80 | "source": [] 81 | } 82 | ], 83 | "metadata": { 84 | "kernelspec": { 85 | "display_name": "Python 3", 86 | "language": "python", 87 | "name": "python3" 88 | }, 89 | "language_info": { 90 | "codemirror_mode": { 91 | "name": "ipython", 92 | "version": 3 93 | }, 94 | "file_extension": ".py", 95 | "mimetype": "text/x-python", 96 | "name": "python", 97 | "nbconvert_exporter": "python", 98 | "pygments_lexer": "ipython3", 99 | "version": "3.8.6" 100 | } 101 | }, 102 | "nbformat": 4, 103 | "nbformat_minor": 2 104 | } 105 | -------------------------------------------------------------------------------- /Homework_1_problem1.2.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "markdown", 5 | "metadata": {}, 6 | "source": [ 7 | "# Homework 1 Problem 1.2\n", 8 | "\n", 9 | "There are of course \"many ways to skin a cat\", as the unpleasant saying goes, but here are two free alternatives to using Mathematica on your own system to help you with some of the tricky bits in solving your homework integrals. \n", 10 | "\n", 11 | "We are trying to get an answer for the integral:\n", 12 | "$$I =\\int_{-\\infty}^{\\infty} A e^{-\\lambda\\left(x-a\\right)^2}dx$$\n", 13 | "\n", 14 | "One way to get the answer is to ask Wolfram Alpha: `Integrate[A E^(-l (-a + x)^2), {x, -Infinity, Plus[Infinity]}]` or `integrate from -infinity to +infinity A*exp(-l*(x-a)**2)`, which indeed provides the answer. \n", 15 | "\n", 16 | "The other way is to use sympy, which has documentation here: [Sympy](http://docs.sympy.org/latest/index.html)\n", 17 | "\n", 18 | "First, import sympy, and since we want to plot the function, also import matplotlib.pyplot.\n" 19 | ] 20 | }, 21 | { 22 | "cell_type": "code", 23 | "execution_count": 1, 24 | "metadata": { 25 | "collapsed": true 26 | }, 27 | "outputs": [], 28 | "source": [ 29 | "from sympy import *\n", 30 | "import matplotlib.pyplot as plt" 31 | ] 32 | }, 33 | { 34 | "cell_type": "markdown", 35 | "metadata": {}, 36 | "source": [ 37 | "Next, we want to tell sympy what symbols we want to use, and that we have a function `rho(x)` which we will integrate. An important part is to tell sympy the assumption that all the variables are real numbers, and that lambda (`lam`) is postitive. If we don't do this step, the output will be hard to read because of all the conditions on the integral." 38 | ] 39 | }, 40 | { 41 | "cell_type": "code", 42 | "execution_count": 2, 43 | "metadata": { 44 | "collapsed": true 45 | }, 46 | "outputs": [], 47 | "source": [ 48 | "A, lam, a, x = symbols(\"A lam a x\",real=True)\n", 49 | "assumptions.assume.global_assumptions.add(Q.positive(lam))\n", 50 | "rho = Function('rho')(x)\n", 51 | "rho = A*exp(-lam*(x-a)**2)" 52 | ] 53 | }, 54 | { 55 | "cell_type": "markdown", 56 | "metadata": {}, 57 | "source": [ 58 | "We now integrate the function from minus to plus infinity:" 59 | ] 60 | }, 61 | { 62 | "cell_type": "code", 63 | "execution_count": 3, 64 | "metadata": {}, 65 | "outputs": [ 66 | { 67 | "data": { 68 | "text/plain": [ 69 | "Piecewise((sqrt(pi)*A/sqrt(lam), Abs(periodic_argument(lam, oo)) <= pi/2), (Integral(A*exp(-lam*(-a + x)**2), (x, -oo, oo)), True))" 70 | ] 71 | }, 72 | "execution_count": 3, 73 | "metadata": {}, 74 | "output_type": "execute_result" 75 | } 76 | ], 77 | "source": [ 78 | "integrate(rho,(x,-oo,oo))" 79 | ] 80 | }, 81 | { 82 | "cell_type": "markdown", 83 | "metadata": {}, 84 | "source": [ 85 | "So the answer we got for the integral is \n", 86 | "$$ \\frac{\\sqrt{\\pi} A}{\\sqrt{\\lambda}}$$\n", 87 | "We want to equate this to 1, and then solve for $A$, which gives us:\n", 88 | "$$ A = \\sqrt{\\frac{\\lambda}{\\pi}}$$\n", 89 | "We redefine rho so that A is eliminated. Note that this is easier than requesting sympy to substitute for A all the time." 90 | ] 91 | }, 92 | { 93 | "cell_type": "code", 94 | "execution_count": 4, 95 | "metadata": { 96 | "collapsed": true 97 | }, 98 | "outputs": [], 99 | "source": [ 100 | "rho = sqrt(lam/pi)*exp(-lam*(x-a)**2)" 101 | ] 102 | }, 103 | { 104 | "cell_type": "markdown", 105 | "metadata": {}, 106 | "source": [ 107 | "We can now do the rest of the homework. Integrate x*rho and x*x*rho:\n", 108 | "$$\\left< x \\right> = \\int_{-\\infty}^\\infty x \\sqrt{\\frac{\\lambda}{\\pi}}e^{-\\lambda(x-a)^2} dx$$\n", 109 | "$$\\left< x^2 \\right> = \\int_{-\\infty}^\\infty x^2 \\sqrt{\\frac{\\lambda}{\\pi}}e^{-\\lambda(x-a)^2} dx$$" 110 | ] 111 | }, 112 | { 113 | "cell_type": "code", 114 | "execution_count": 5, 115 | "metadata": {}, 116 | "outputs": [ 117 | { 118 | "name": "stdout", 119 | "output_type": "stream", 120 | "text": [ 121 | "Piecewise((a, (Abs(periodic_argument(lam, oo)) <= pi/2) & (Abs(periodic_argument(lam, oo)) < pi/2)), (Integral(sqrt(lam)*x*exp(-lam*(-a + x)**2)/sqrt(pi), (x, -oo, oo)), True))\n", 122 | "Piecewise((a**2 + 1/(2*lam), (Abs(periodic_argument(lam, oo)) <= pi/2) & (Abs(periodic_argument(lam, oo)) < pi/2)), (Integral(sqrt(lam)*x**2*exp(-lam*(-a + x)**2)/sqrt(pi), (x, -oo, oo)), True))\n" 123 | ] 124 | } 125 | ], 126 | "source": [ 127 | "print integrate(x*rho,(x,-oo,oo))\n", 128 | "print integrate(x*x*rho,(x,-oo,oo))" 129 | ] 130 | }, 131 | { 132 | "cell_type": "markdown", 133 | "metadata": {}, 134 | "source": [ 135 | "The results are $\\left< x \\right> = a$ and $\\left< x^2 \\right> =a^2 + 1/({2\\lambda})$ so we conclude that:\n", 136 | "$$\\sigma^2 = \\left< x^2\\right> - \\left< x \\right>^2 = 1/({2\\lambda}) \\Rightarrow\\\\\n", 137 | "\\sigma = \\sqrt{\\frac{1}{2\\lambda}} \\Rightarrow \\\\\n", 138 | "\\lambda = \\frac{1}{2\\sigma^2}\n", 139 | "$$\n", 140 | "We can thus write the normalized gaussian function in terms of $\\sigma$ as:\n", 141 | "$$\n", 142 | "\\rho(x) = \\sqrt{\\frac{1}{2\\pi\\sigma^2}} e^{-(x-a)^2/{2\\sigma^2}}\n", 143 | "$$\n", 144 | "We now write `rho` as a function `rho_f`, which allows us to evaluate it at many points and make a graph. Choose `a=4` and `sigma=1`. We want to evaluate the function *numerically* which means we don not want the `sqrt()` and `exp()` functions from sympy. This is a disadvantage of importing sympy with `from sympy import *`. We can explicitly ask for the numpy versions of these functions to get numeric results." 145 | ] 146 | }, 147 | { 148 | "cell_type": "code", 149 | "execution_count": 6, 150 | "metadata": { 151 | "collapsed": true 152 | }, 153 | "outputs": [], 154 | "source": [ 155 | "import numpy as np\n", 156 | "def rho_f(x,a,sig):\n", 157 | " return( np.sqrt(1/(2*np.pi*sig**2)*np.exp(-(x-a)**2/2/sig**2)))" 158 | ] 159 | }, 160 | { 161 | "cell_type": "markdown", 162 | "metadata": {}, 163 | "source": [ 164 | "We can now evaluate the function and make our plot. We can plot a number of different sigmas on the same graph so you get a sense of how changing sigma changes the curve." 165 | ] 166 | }, 167 | { 168 | "cell_type": "code", 169 | "execution_count": 7, 170 | "metadata": { 171 | "collapsed": true 172 | }, 173 | "outputs": [], 174 | "source": [ 175 | "x_r = np.arange(-2,10,0.01) # Set the range in x, with a small step size." 176 | ] 177 | }, 178 | { 179 | "cell_type": "code", 180 | "execution_count": 19, 181 | "metadata": {}, 182 | "outputs": [], 183 | "source": [ 184 | "plt.figure(figsize=(10,5))\n", 185 | "x_ave = 4\n", 186 | "for s in [0.5,1,2]:\n", 187 | " p = plt.plot(x_r,rho_f(x_r,x_ave,s),label=\"sigma={}\".format(s))\n", 188 | " x1 = x_ave-s # Draw lines\n", 189 | " x2 = x_ave-s\n", 190 | " plt.plot([x1, x2], [-0.05, 0.1],color=p[0].get_color(), linestyle='-', linewidth=3)\n", 191 | " x1 = x_ave+s\n", 192 | " x2 = x_ave+s\n", 193 | " plt.plot([x1, x2], [-0.05, 0.1],color=p[0].get_color(), linestyle='-', linewidth=3)\n", 194 | " plt.legend() \n", 195 | " plt.title(\"Normalized Gaussian with a=4\")\n", 196 | " plt.xlabel(\"x\")\n", 197 | " plt.ylabel(\"y\")\n", 198 | " plt.grid(True,which='both')" 199 | ] 200 | }, 201 | { 202 | "cell_type": "code", 203 | "execution_count": 20, 204 | "metadata": { 205 | "collapsed": true 206 | }, 207 | "outputs": [], 208 | "source": [ 209 | "plt.savefig('Homework_1p1_2.pdf',format='pdf') # Save the figure to a file, so you can print it separately." 210 | ] 211 | }, 212 | { 213 | "cell_type": "code", 214 | "execution_count": 21, 215 | "metadata": {}, 216 | "outputs": [ 217 | { 218 | "data": { 219 | "image/png": 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Bb/x5DT96YzNpfaIY3qf9E0eK+IuztWR5y6FDh4iLi+PWW28lJibmpAH9kyZN4p577qG4\nuJjIyEjeeOMNxowZ0+pjl5WVERERQXR0NEePHmXZsmVNrYhPPvnkWT97+eWX8+c//5m5c+eyevVq\noqOj6du370n7uFwuSkpKSEhIoK6ujnfffZdLLrmk9V++lbw6hsxauxRnsH7z937W7Pl2YLo3axAR\nabQip4C/rjrA7dMHccOEU8NYo7DgQP5n3jiu+P2n3P3KBt69ewYhQZpHW6SttmzZwv33309AQADB\nwcE8/fTT3HfffYDT+vTggw8yefJk4uLiSEtLIzo6utXHTk9PZ9y4caSlpZGcnMz06a2PFbNnzyYr\nK4uhQ4cSHh7OX/7yl6ZtGRkZZGdnc+LECWbPnk1dXR319fVccskl3Hnnna3/8q3k60H9IiIdoqau\nnh//bQtDekXww8uGn3P/3pFh/PbGMdz+3Dqe/XQfCzOHdECVIl3T7NmzmT179knvNR/8Pm/ePBYs\nWIDL5eK6667j2muvBeC5555r2iclJYWtW7c2vW6+rfnz82GMOeM4s+zsbAAiIiJYv359m45/PvS/\nfCLSLTz76T7yS6r55bWjCQtu3R2UF6clcunIRP7wz10cLq32coUi3dcjjzxCRkYGo0ePZtCgQU2B\nrDtRC5mIdHlFlbX87/LdXDoykQuGJJzXZ386ZyQX/1cWTy3fzaPXtn5ci4i03hNPPOHrEnxOLWQi\n0uX9ZeU+qurqW9VV2VJyXDg3TUxmydpc8oqrvFCdiIgCmYh0ceU1dTz/2X4uHZnI0N5tu1vyu18Z\nisHwzIq9Hq5ORMShQCYiXdrLqw9SVuPiO5lD23yMfjE9uCq9H6+vz6O0us6D1YmIOBTIRKTLqm+w\nPP/Zfi4YEk96cky7jvXN6SlU1dbz2rrcc+8sInKeFMhEpMvK2nmMQ6U13DZtYLuPNbp/NJNT4nju\ns/3UawFykXa744472L59u09ryMnJYdq0aYSGhvr8xgIFMhHpsl5efZBekaHMGpHokeN9c3oKecXV\nfJxz7Nw7i8hZLVq0iJEjR/q0htjYWP7whz80TVLrSwpkItIlHSqpZvnOY9w0MYngQM/8qJs1IpG4\niBDeWJ/vkeOJdBeVlZVceeWVpKenM3r0aJYsWUJmZibr1q0D4NlnnyU1NZXJkydz5513ctdddwEw\nf/58Fi5cyNSpUxk8eDBZWVncfvvtjBgxgvnz5zcdf+HChUycOJFRo0bx8MMPt7quXr16MWnSJIKD\ngz36fdtC85CJSJf0+vo8LDB30gCPHTMkKIBrMvrx0ucHKamqJSY8xGPHFunK3n//ffr168d7770H\nQGlpKU8//TTgrHP5y1/+kg0bNhAZGcnFF19Menp602eLi4tZtWoVb7/9NldffTUrV65k0aJFTJo0\niezsbDIyMnjssceIi4ujvr6eWbNmsXnzZsaOHXvOxcX9iQKZiHQ51lrezM5nyqA4kuPCPXrsGyck\n8ZeV+3ln0yG+Pi3Fo8cW6RDLHoAjWzx7zD5j4PLfnHHzmDFjuPfee/nRj37EnDlzmDFjRtO2NWvW\nMHPmTOLi4gD46le/Sk5OTtP2q666CmMMY8aMITExsWnh8VGjRrF//34yMjJ49dVXeeaZZ3C5XBw+\nfJjt27czduzYcy4u7k8UyESky9l2qIy9BZXcOWOwx489ql80aX0ieX1DvgKZSCulpqayYcMGli5d\nykMPPcSsWbNa/dnQ0FAAAgICmp43vna5XOzbt48nnniCtWvXEhsby/z586mpqQFQC5mIiC+9lZ1P\ncKDh8tF9vHL868b159fLviC3qMrjLXAiXneWlixvOXToEHFxcdx6663ExMSwaNGipm2TJk3innvu\nobi4mMjISN54442mVrDWKCsrIyIigujoaI4ePcqyZcvIzMwEUAuZiIiv1DdY3t50iJmpvb02xuuK\nMX359bIvWLrlMP8+c4hXziHSlWzZsoX777+fgIAAgoODefrpp5vubOzfvz8PPvggkydPJi4ujrS0\nNKKjo1t97PT0dMaNG0daWhrJyclMnz691Z89evQoI0aMoKysjICAAP77v/+b7du3ExUVdd7fsb0U\nyESkS9lwsJijZSf4yZX9vHaO5LhwxiZFK5CJtNLs2bOZPXv2Se9lZWU1PZ83bx4LFizA5XJx3XXX\nce211wLw3HPPNe2TkpLC1q1bm14339b8+flITEwkLy+vTZ/1NE17ISJdyofbjhASGMBXhvfy6nmu\nGNOXTXml5BZpwXGR9nrkkUfIyMhg9OjRDBo0qCmQdSdqIRORLsNay4fbjzJtSDyRYd6dV+jKMX35\nzbIvWLb1MAsuUiuZSHv4epZ8f6AWMhHpMnYdq+BAYRWXjvLMzPxnkxwXzsi+UXy0XbP2i0j7KZCJ\nSJfx4bYjAPybh5ZKOpdLRvRm3YEiSqpqO+R8ItJ1KZCJSJfx4fajZCTH0DsqrEPOd/GIRBosfJxT\n0CHnE5GuS4FMRLqEw6XVbM4r7ZDuykZj+0eT0DOEj3ao21JE2keBTES6hOVfOK1Ul3RQdyVAQIDh\nK8N78/HOY9TVN3TYeUW6gjvuuIPt27f7tIYlS5YwduxYxowZwwUXXMCmTZt8VosCmYh0CStyCugb\nHcaw3j079LyzRvSmrMbF+gPFHXpekc5u0aJFjBw50qc1pKSk8PHHH7NlyxZ++tOfsmDBAp/VokAm\nIp2eq76BlXuOc9GwXhhjOvTcFw7rRXCg4Z87jnboeUU6k8rKSq688krS09MZPXo0S5YsITMzk3Xr\n1gHw7LPPkpqayuTJk7nzzju56667AJg/fz4LFy5k6tSpDB48mKysLG6//XZGjBjB/Pnzm46/cOFC\nJk6cyKhRo3j44YdbXdeUKVOIjY0FYOrUqT6dJFaBTEQ6vU15JZTXuLgo1buTwZ5Oz9AgJg+KY0XO\n8Q4/t0hn8f7779OvXz82bdrE1q1bueyyy5q2HTp0iF/+8pd8/vnnrFy5ki+++OKkzxYXF7Nq1Sqe\nfPJJrr76ar7//e+zbds2tmzZQnZ2NgCPPfYY69atY/PmzXz88cds3rwZcBYXz8jIOOXxm9+cup7n\ns88+y+WXX+7Fq3B2mhhWRDq9j3OOE2DgwqEJPjn/hUN78fj7X3CsvIbekR1zh6dIWz2+5nG+KPri\n3Dueh7S4NH40+Udn3D5mzBjuvfdefvSjHzFnzhxmzJjRtG3NmjXMnDmTuLg4AL761a+Sk5PTtP2q\nq67CGMOYMWNITExsWnh81KhR7N+/n4yMDF599VWeeeYZXC4Xhw8fZvv27YwdO7bVi4svX76cZ599\nlk8//bQtX98jFMhEpNNbkVNAenIM0eHenZ3/TC4cmsDjwMrdx7luXJJPahDxZ6mpqWzYsIGlS5fy\n0EMPMWvWrFZ/NjQ0FICAgICm542vXS4X+/bt44knnmDt2rXExsYyf/58ampqAKeFbPny5accc+7c\nuTzwwAMAbN68mTvuuINly5YRHx/fnq/ZLgpkItKplVTVsjmvhLsvHuazGkb1iyImPJhPdxUqkInf\nO1tLlrccOnSIuLg4br31VmJiYli0aFHTtkmTJnHPPfdQXFxMZGQkb7zxRlMrWGuUlZURERFBdHQ0\nR48eZdmyZWRmZgKcs4UsNzeX66+/nhdeeIHU1NQ2fTdPUSATkU7t093HabBwUapvuivBmf5i+pAE\nVu4+jrW2w28sEPF3W7Zs4f777ycgIIDg4GCefvpp7rvvPgD69+/Pgw8+yOTJk4mLiyMtLY3o6OhW\nHzs9PZ1x48aRlpZGcnIy06dPb/VnH3/8cQoLC/nOd74DQFBQUNONBh1NgUxEOrUVOQVEhgWRnhTj\n0zouHJbAe1sOs6eggqG9I31ai4i/mT17NrNnzz7pvaysrKbn8+bNY8GCBbhcLq677jquvfZaAJ57\n7rmmfVJSUti6dWvT6+bbmj8/H3/84x95/vnn2/RZT9NdliLSaVlrWbm7kOlDEggK9O2Ps8YbCj7d\npbstRc7XI488QkZGBqNHj2bQoEFNgaw7UQuZiHRaecXV5JdU8+8zB/u6FJLjwhkQF86nuwuZP32Q\nr8sR6VSeeOIJX5fgc2ohE5FOa9XeQgCmDvbdnVHNXTgsgc/3FmoZJRE5bwpkItJpfb6nkPiIkA5f\nLulMLhyaQMUJF5vzSnxdisgprLW+LqFLa+/1VSATkU7JWsvnewuZOjjeb+5qnDLImdhy9b4iH1ci\ncrKwsDAKCwsVyrzEWkthYSFhYW2fGFpjyESkU8otquZQaQ0LB8f5upQm8T1DGda7J6v3FvGdTF9X\nI/KlpKQk8vLyKCgo8HUpfqWmpqZdIaq5sLAwkpLaPg+hApmIdEqr9jp3M/rL+LFGUwbH8ebGQ7jq\nG3x+56dIo+DgYAYN0s0mLWVlZTFu3DhflwGoy1JEOqnP9xYRHxHCUD8ZP9Zo8qB4Kk642H64zNel\niEgnokAmIp2OP44fa9Q4jmyNxpGJyHlQIBORTudgURWHS2uYOsS/uisBEqPCSIkP5/O9CmQi0noK\nZCLS6ax2h52pg/xnQH9zUwbFs3Z/EQ0NuqNNRFpHgUxEOp21+4uIDQ/2u/FjjaYMjqO0uo6dR8t9\nXYqIdBIKZCLS6aw/UMyEgbF+N36s0eTG+cjcKwmIiJyLApmIdCrHK06w93glEwb6Z3clQFJsOP1j\nemiCWBFpNQUyEelU1h8oBmBSSqyPKzm7yYPiWHegWDOji0irKJCJSKey/kAxIYEBjO4f7etSzmr8\nwFgKyk+QV1zt61JEpBNQIBORTmXt/iLGJEUTFhzo61LOauJApwWvsUVPRORsFMhEpNOoqatna35p\nU9jxZ6mJkfQMDVIgE5FW8WogM8ZcZozZaYzZbYx54Az73GSM2W6M2WaMedmb9YhI57Y5r5S6esvE\nFP8d0N8oMMAwbkAM6xTIRKQVvBbIjDGBwFPA5cBI4GZjzMgW+wwDfgxMt9aOAu7xVj0i0vmtO+Dc\ntTihE7SQAYwfEMvOI2WU19T5uhQR8XPebCGbDOy21u611tYCi4FrWuxzJ/CUtbYYwFp7zIv1iEgn\nt25/MYN7RRAXEeLrUlplwsBYGixsyi31dSki4ue8Gcj6A7nNXue532suFUg1xqw0xnxujLnMi/WI\nSCfW0GBZf6CYSX48/1hL4wbEYIwG9ovIuQX5wfmHAZlAErDCGDPGWlvSfCdjzAJgAUBiYiJZWVle\nLaqiosLr5+hudE09r7td0/yKBkqr6+hZc9Qr39tb1zOpZwD/2LiH9KB8jx/b33W3P6MdQdfUs/zp\nenozkOUDyc1eJ7nfay4PWG2trQP2GWNycALa2uY7WWufAZ4BmDhxos3MzPRWzQBkZWXh7XN0N7qm\nntfdrunLqw8CW7hl9jQG9/L8Gpbeup4XFW/h7exDzLhoJoEB/rnUk7d0tz+jHUHX1LP86Xp6s8ty\nLTDMGDPIGBMCzAXebrHPmzitYxhjEnC6MPd6sSYR6aTWHSgiPiKEQQkRvi7lvEwYGEv5CRe7jmmh\ncRE5M68FMmutC7gL+ADYAbxqrd1mjPmFMeZq924fAIXGmO3AcuB+a61W4xWRU2w8WMK4Af67oPiZ\nTHSPedM4MhE5G6+OIbPWLgWWtnjvZ82eW+AH7oeIyGkVV9ay73glN05I8nUp5y05rgcJPUNZv7+Y\nW6YM9HU5IuKnNFO/iPi97DznPp9xA2J8XMn5M8YwYWAM6w+qhUxEzkyBTET8XvbBEoyBsUmdL5CB\nM47sQGEVBeUnfF2KiPgpBTIR8XvZuSWk9nbWhuyMxg9wVhbIzi05x54i0l0pkImIX7PWkp1b0im7\nKxuN7h9NUIBho7otReQMFMhExK/tO15JaXUdGcmdN5CFBQeS1jdSLWQickYKZCLi1zYebBzQ3zkW\nFD+TjOQYNueVUt9gfV2KiPghBTIR8WvZuSVEhAQytLfnZ+fvSOOSY6k44WJPQYWvSxERP6RAJiJ+\nLTu3hLFJMZ1+2aEM9xi47IPqthSRUymQiYjfqqmrZ8fhsk49oL/RoPgIosKC2Jirgf0icioFMhHx\nW1vzS3E12E49oL9RQIAhPTmmaUyciEhzCmQi4rca70rM6AItZODcmJBztJzKEy5flyIifkaBTET8\n1saDJfQ6afFQAAAgAElEQVSP6UHvyDBfl+IR45JjaLCwJb/U16WIiJ9RIBMRv5WdW9JlWscA0t1d\nr+q2FJGWFMhExC8dK6shv6SacV1g/FijuIgQBsaHk62B/SLSggKZiPiljbmNE8J2nUAGTrelZuwX\nkZYUyETEL2XnlhAUYBjVL9rXpXhURnIMR8tOcLi02teliIgfUSATEb+08WAxI/tFERYc6OtSPCrD\nvQSUJogVkeYUyETE79Q3WDbnlXaJ+cdaGtE3kpDAgKYuWRERUCATET+Uc7Scqtr6Ljd+DCA0KJBR\n/aPUQiYiJ1EgExG/0zQhbHKsjyvxjozkGLbkl+Kqb/B1KSLiJxTIRMTvZB8sISY8mJT4cF+X4hUZ\nyTFU19Wz82i5r0sRET+hQCYifmdjbjEZyTEYY3xdileMc7f8aYJYEWmkQCYifqW8po5dxyq65ID+\nRslxPYiLCNF8ZCLSRIFMRPzK5rxSrKVLBzJjjCaIFZGTKJCJiF/5ckB/1w1k4Hy/PQUVlNXU+boU\nEfEDCmQi4lc2HixhcEIEMeEhvi7FqzIGxGAtbM4t9XUpIuIHFMhExG9Ya8nOLenyrWMAY5Oc76iF\nxkUEFMhExI/kl1RzvOIEGV1wQtiWonsEM6RXhMaRiQigQCYifqS7jB9rlJEcS3ZuCdZaX5ciIj6m\nQCYifmNTbgkhQQGk9YnydSkdImNADMcraskrrvZ1KSLiYwpkIuI3snNLGNUvipCg7vGjaZy7JVAL\njYtI9/ipJyJ+r66+gS35pd2muxJgeJ9IQoMCtNC4iCiQiYh/2HmknJq6hm4VyIIDAxjTP1p3WoqI\nApmI+IdNed1rQH+jcQNi2HqojFpXg69LEREfUiATEb+QfbCEuIgQBsSF+7qUDpWRHEutq4EvjpT5\nuhQR8SEFMhHxC9m5JaQnRWOM8XUpHapxzjXNRybSvSmQiYjPldfUsbuggozkWF+X0uH6RYfRKzJU\nA/tFujkFMhHxuS15pVhLt5ihvyVjDBnJMWohE+nmFMhExOca5+FKT4r2cSW+kZEcw97jlZRU1fq6\nFBHxEQUyEfG57NwSBiVEEBMe4utSfKJxgli1kol0XwpkIuJT1lqyc0u63XQXzY1JisYYBTKR7kyB\nTER86nBpDQXlJ7p1IIsMC2ZY754KZCLdmAKZiPhUYwhJ78aBDJxxZJtyS7DW+roUEfEBBTIR8ans\n3BJCAgMY0TfS16X4VEZyLMVVdRworPJ1KSLiAwpkIuJT2QdLGNkvitCgQF+X4lMZGtgv0q0pkImI\nz7jqG9iSX9qtx481Sk3sSXhIoAKZSDelQCYiPpNztILqunrGdcMJYVsKCgxgTP/opjnZRKR7USAT\nEZ9pGtCfpEAGzkoFOw6VccJV7+tSRKSDKZCJiM9k5xYTGx7MwPhwX5fiF8Ylx1Bb38D2Q2W+LkVE\nOpgCmYj4zKbcUtKTYzDG+LoUv9C4uPpGLTQu0u14NZAZYy4zxuw0xuw2xjxwlv1uMMZYY8xEb9Yj\nIv6j4oSLnGPlGtDfTJ/oMPpEhWlgv0g35LVAZowJBJ4CLgdGAjcbY0aeZr9I4D+A1d6qRUT8z+a8\nEqxFgayFjOQYBTKRbsibLWSTgd3W2r3W2lpgMXDNafb7JfA4UOPFWkTEz/jFgP6GeqgugZJcQmsK\noPwonCgHH86WnzEghoNFVRRWnPBZDSLS8YK8eOz+QG6z13nAlOY7GGPGA8nW2veMMfef6UDGmAXA\nAoDExESysrI8X20zFRUVXj9Hd6Nr6nmd/Zr+Y0MNieGGTWs/8/7JbAPhVXlEleUQVZZDeFUePaqP\nEFpb2LTLNIDPneeuwDBOhCZQ3aMvFT0HUx45hNLoUbiCe3q/1iLnDssXln5CRm9v/oj2vs7+Z9Qf\n6Zp6lj9dT5/9bTfGBAC/A+afa19r7TPAMwATJ060mZmZXq0tKysLb5+ju9E19bzOfE2ttdz36Udc\nlNaHzMwM75ykvg52/xN2vgc5H0LFEef9sGjoNQJS0iEm2Xkd0pMvcnaRNmQg1FYSVH6EoLJ8Igp2\nknDwNbANYAKg/wRInQ2jb4S4QV4pe9IJF79d+wENMclkZg73yjk6Smf+M+qvdE09y5+upzcDWT6Q\n3Ox1kvu9RpHAaCDLfYdVH+BtY8zV1tp1XqxLRHwst6ia4xW1jB8Q6/mDF+TAxhdg02KoPAYhkTB0\nFgy9BAZMhbghEHDqaI0j5VmkTc489Xi1lXAoG/ZmwZ5/wb8edR7JU2DcrTDmJggO81j5EaFBpCZG\naoJYkW7Gm4FsLTDMGDMIJ4jNBeY1brTWlgIJja+NMVnAfQpjIl3f+oNFAEwY6MFAlrsWPv0d7FwK\nAUGQehlk3OIEsaCQth83JAJSpjuPi38CJQdhy+uweQm8fTd89HOYfCdMuhMi4j3yVcYNiOW9zYdo\naLAEBGhKEJHuwGuD+q21LuAu4ANgB/CqtXabMeYXxpirvXVeEfF/Gw6U0NPdEtRu+Rvg+avg2Uvg\nwGcw8wH4wQ6Y+xKkXdG+MHY6MQNgxg/gO5/DbW873ZhZv4bfj4Ws3zg3BbTTuOQYympc7Cus9EDB\nItIZeHUMmbV2KbC0xXs/O8O+md6sRUT8x4aDxaQnRxPYntaf0jz45y+clqrweLj0MZgwH0I7YOA9\ngDEweKbzOPYFLH/UCWZr/gRfeRAmfPO0XaOtkeFe2zP7YAlDenXQ9xERnzrnTwtjzN3GGC8M9BCR\n7qjyhIsvjpS3ffxYQz2s+l/44yTY9iZc+H343ka44K6OC2Mt9U6Dr70Id/wTeg2H934Az/4bHN7c\npsMN6dWTnqFBbMwt9nChIuKvWvO/b4nAWmPMq+6Z9zWgQUTabFNeCfUNlvFtGT92bAc8eyl88GNI\nmQF3r4NLHnHulPQHSRNh/ntw/Z+g5AA8MxP+8TNwnd+cYoEBhrFJ0ZogVqQbOWcgs9Y+BAwDnsWZ\nomKXMeZXxpghXq5NRLqgxnUaxyefRyBraICVf4D/NwOK98H1i2DeEmc8l78xBsbeBHetde7CXPl7\n+NMsJ0yeh/EDYtlxuJzKEy4vFSoi/qRVAxystRY44n64gFjgdWPMb71Ym4h0QRsOFDOkVwTR4cGt\n+0DFMXjpRvjHT2H4ZfDdtTD2q07w8Wc9YuHq/4GbF0P5Yfi/mfD5061eBWBCSiz1DZZNaiUT6RZa\nM4bsP4wx64HfAiuBMdbahcAE4AYv1yciXYi1lg0Hi1s/3cXeLHh6OhxYCVf+Dm56wWNTS3SY4Zc7\nd2QOuRjefwBem9+qOzHHD4jFGFh3QOPIRLqD1txlGQdcb6090PxNa22DMWaOd8oSka5o3/FKiqvq\nzj2g31r4/H/hw4cgfhjc9iYkjuqYIr2hZy+4+RX47H/go4ed7suvvQi9Us/4kegewaT2jlQgE+km\nWjOG7OGWYazZtvMbFCEi3dqGxvFjZ2shq6uBNxfCBw/C8Cvgzn917jDWyBiY/j247S2oKoQ/XQw7\n3z/rR8YPjGXjgWIaGny32LmIdAyvTQwrItLShoPFRIYFMfRMc2tVHIPnroBNr0Dmg04Xpa+msvCW\nQRfBv6+A+CGw+GZY/cwZd504MJbyEy5yjrV/slkR8W8KZCLSYTYcKGbcgNjTLwdUuMeZu+vodqc7\nL/NHbZ5Y1e9F94dvLnWWd1p2P7z/Y2d+tRYmpjgtiev2q9tSpKvroj/tRMTflNfUsfNoOePds9Cf\nJG+9E8ZqymD+uzDiqo4vsKOFRDjBc8pCZ7zckq9DbdVJuwyICyehZyjrNY5MpMtTIBORDrEptxRr\nOXVAf84H8PwcCOkJ3/qHM7lqdxEQCJf/Bi573FkU/aUbnVDqZoxh4sBY1h0o8mGRItIRFMhEpEOs\n3V+EMV+u0wjA1r/B4nmQMAzu+AgShvquQF+a+m24YRHkroa/Xg2VhU2bJgyMJbeommNlNT4sUES8\nTYFMRDrE2v1FjOgTRVSYe0LYTYvhjW9B0iT4xrvQs7dvC/S1MTfC115ypsR47gooOwQ4E8QC6rYU\n6eIUyETE6+rqG9h4sITJg+KcN9Y/D3//NqRcCLe+AWFRvi3QXwy/DG55HUrz4M+XQUkuo/tFExoU\noPnIRLo4BTIR8bqt+aVU19UzKSUO1vwJ3vkeDJ0F8151BrfLlwbNgNvehuoSeH4OIZWHSE+KUSAT\n6eIUyETE69budwalX1T6Jiy9D4ZfCXNfhuAePq7MTyVNgK//HaqK4Lk5zOxXx7b8UqprT50aQ0S6\nBgUyEfG6NfuK+XbUKiL/+QCkXg43PQ9Bob4uy78lTYBb/waVx/lmzt3ENRSxKU8LjYt0VQpkIuJV\nDQ2W+P3v8MPap5wFtr/6HAQG+7qsziF5Etz6Bj1OFPBKyKPs2LXL1xWJiJcokImIVx1e8zqPNfyB\n43HjnbsIg8N8XVLnMmAK5ut/o19AEbPWLYRqjSUT6YoUyETEe3Z9RJ8PFrLFDqb6xpchJNzXFXVO\nA6byyuDf0Lf2APalm6C20tcViYiHKZCJiHccWAVLbuFwyEB+EPIzBvTt5vOMtVNC+mV8r+4uyF/n\nLLPkqvV1SSLiQQpkIuJ5R7fDK1+D6GQW2J8wclAyxpxmQXFptamD4ljWMIUVwx+CPf+Ev9152gXJ\nRaRzUiATEc8qyYUXb4CgHhy++iW2l4UyKSX23J+Ts+odFcbghAj+WnMRXPoobH8T3v0+WOvr0kTE\nAxTIRMRzqorgxeudMU63vsHnRc6kr5MaZ+iXdpkyOI41+4uon3oXzLgXNjwP/3rU12WJiAcokImI\nZ9RWwcs3QfEBuPkV6DOaNfuKiQwNIq2PlkbyhCmD4imvcbHjcBlc/FMY93X45AlY9xdflyYi7aRA\nJiLtV18Hr82H/PVwwyJImQ7Amn2FTEiJJTBA48c8Ycpgp6Xx872FYAzMeRKG/hu89wPY+b6PqxOR\n9lAgE5H2sRbeuQd2fQBXPAEjrwbgaFkNewoquWBIvI8L7Dr6RvdgYHw4q/c5S1ERGOxMtNtnDLz+\nTScQi0inpEAmIu3z8W8h+0WY+SOY9K2mt1ftKQTggiEJvqqsS5o6KJ41+4poaHAP5g/tCfNeg4gE\neOkmKNrr2wJFpE0UyESk7TYtgaxfQfo8yPzxSZtW7SkkKiyIEX01fsyTpgyOo7S6ji+OlH/5ZmSi\ns+6lrYcXb4TKQt8VKCJtokAmIm2zfyW8fRekzICrfu+MaWrms73HmTo4XuPHPGzKYKcLePW+FqEr\nYRjcvBhK85w54GqrfFCdiLSVApmInL/ju2HJLRAzEL72AgSFnLQ5t6iK3KJqjR/zgv4xPUiO68Hq\nvUWnbhwwFW74E+Stc08c29DxBYpImyiQicj5qSyEl78KJhBueQ16nDrp66q97vFjQzV+zBumDIpn\n9b7CL8eRNTfyGpj9K/jiXfjnIx1em4i0jQKZiLReXQ0sngel+c5cY3GDTrvbqj2FJPQMYVjvnh1c\nYPcwbXA8xVV17DhSdvodpi6ESXfAyt/D+uc6tDYRaRsFMhFpHWvhre9C7udw3f+D5Mln2M3y2R5n\n/JjWr/SOC4c5LY8rdx8//Q7GwGWPw9BL4L17Yc/yDqxORNpCgUxEWmf5r2Dr6zDrYRh9/Rl323e8\nkqNlJzTdhRclRoWRmtiTT3adIZABBAbBjX+BhFR49RtQsLPjChSR86ZAJiLnlv0yrPits1TPhd8/\n666fuecfm6YB/V41fWgCa/YVUVNXf+adwqJg3hIICoWXvgqVZwlwIuJTCmQicnb7VsDb34NBM52l\nes7RDblqTyF9o8NIiQ/voAK7pxnDEjjhamD9geKz7xgzwJkOo+KoM/6vrqZjChSR86JAJiJnVpAD\nS26F+CFw01+dpXrOor7B8unu40wfmqDxY142ZVA8wYHm7N2WjZImwHX/B7mr4a3vOOMBRcSvKJCJ\nyOlVHoeXboTAEJj3KvSIOedHNueVUFpdx0WpvTqgwO4tIjSIcQNizzywv6VR18Ilj8DWNyDr194s\nTUTaQIFMRE5VVwOv3Ox0c928BGIHtupjK3KOYwzM0PxjHWLG0AS2HiqluLK2dR+Yfg+MuxU+fhw2\nLfZucSJyXhTIRORkDQ3w5kLIWwPXP+N0d7XSil0FjO0fTWxEyLl3lnabPiwBa2Hlnla2khkDVz7p\nLHf11l3O8lci4hcUyETkZMsfg21/g0t+7sz63kql1XVk55aou7IDje0fTWRYEJ+2ZhxZo6AQZ7mr\n2BRn+avCPV6rT0RaT4FMRL608SX45AkYfxtM/4/z+uhnu49T32AVyDpQUGAAFwyJ55Ndx7HnM1C/\nRyzc8ipgnOkwqk6zLqaIdCgFMhFx7PsE3vkPZ3qLK393zuktWlqxq4DI0CAyks89+F8856LUXuSX\nVLOnoOL8Phg3GOa+DKW5zp20rhPeKVBEWkWBTETg+C7nH+W4wa2a3qIlay0rco5zwdB4ggP1Y6Uj\nZQ7vDcC/vjh2/h8eOA2ufRoOrIS379Z0GCI+pJ+cIt1dZaHTbRUQ5HRjtWJ6i5b2FFSQX1Kt7kof\n6B/Tg7Q+kW0LZABjboSLH4LNSzQdhogPKZCJdGeuE87A7rJDcPMrzkDvNmgMAzMVyHziK2m9Wbe/\nmLKaurYdYMZ9X06Hkf2KZ4sTkVZRIBPprqx1pj44uAquexqSJ7f5UB/tOEZan0iSYrVcki9cnNYb\nV4Plk5w2rlVpDMz5b2f84Nt3O+MJRaRDKZCJdFcfPw5bXnW6q0bf0ObDlFTVsv5AMZeMSPRgcXI+\nxiXHEN0juO3dluCMG7zpr84yWUtugYKdnitQRM7Jq4HMGHOZMWanMWa3MeaB02z/gTFmuzFmszHm\nn8aY1k0HLiLts/lVZ7xQ+jynu6odsnYWUN9gmTWit4eKk/MVFBjAzNRefJxzjIaGdgzM7xHjLJMV\nGOqMK6wo8FyRInJWXgtkxphA4CngcmAkcLMxZmSL3TYCE621Y4HXgd96qx4RcTvwGbz1XRh4IVz1\n+/Oe3qKlj3YcJaFnKOlJmu7Cly5O683xilo255e270CxA2HeYqg4Bq/MhbpqzxQoImflzRayycBu\na+1ea20tsBg4adpva+1ya22V++XnQJIX6xGRgp3OGpUxA53Z2oPat8RRXX0DH+cUcHFaLwIC2hfs\nfOm8JlX1UzNTexFg4F87jrb/YP0nwA1/gvz18LcFznJaIuJVQV48dn8gt9nrPGDKWfb/FrDMi/WI\ndG9lh+HFGyAwBG59HcLj2n3ItfuKKK9xMasDx4/VuGooOVFCcU2x8zhRTMmJEkpPlFJZV0llXSVV\nriqq6qpOel5bX4urwYXLuqhrqHOeN7iot/U0WCdwBP41kAATQKBp9mtAACEBIfQI6nHqI9j5NSok\nipjQGKJDo4kOjXaeh0QTE+a8FxxwfvO6tUVsRAgTU+L4cPtRfnDp8PYfcMRVcOmj8OFP4KOH4dJf\ntv+YInJG3gxkrWaMuRWYCMw8w/YFwAKAxMREsrKyvFpPRUWF18/R3eiaet75XNNAVxUZ2Q8SXlXA\nxnGPUbFpP7C/3TW8vOMEQQHA4R1kFXzRrmPV23rK6ssoqS+hxFXi/Nr8uauEioYKam3tGY8RYkII\nCwgj1IQSGhDa9GusiSXYBBMYGEgggU7QwglcgTjh60TtCYKCg2igAYulwTbQ+J/Luqitr6XWVUuV\nraKkoYRaW0utreVEwwmqG6px4TpjXZEBkUQHRhMVFEV0YHTTIyYwhpigGOKD4ukR0KNd1w9gaGgd\nL++rZfF7/6JPhAc6QOwohvW7nP6f/YGcgloO9b/8vD6uv/eep2vqWf50Pb0ZyPKB5Gavk9zvncQY\ncwnwE2Cmtfa0a3dYa58BngGYOHGizczM9HixzWVlZeHtc3Q3uqae1+prWl/nDNCuPAjzXmXisEs8\ncn5rLT9ds5wLh8Uy+5LWTZlR7aomrzyP3PLcpkfj60MVh3DZk0NNaGAoieGJJEYlMiJ8BHFhccSF\nxRETGkNsWCyxobHEhMUQFxpHZEgkgQGBbf4+7fkzaq2l2lXd1FLX+GvpiVKKaoooqC6goKqAo1VH\n2VW9i8KKQiwnd5PGhMaQ1DOJ/pH9T/p1YNRA+kT0IcCcO2ANK6nm5d/8i5KeA5k7c0ibvsspLpoB\ni+eRuvsZUifMhLQrWv1R/b33PF1Tz/Kn6+nNQLYWGGaMGYQTxOYC85rvYIwZB/wfcJm1th33a4vI\naVnrzCu1dzlc8xR4KIwBbM0vI7eomru/MuyUbWW1Zewt2cuekj3sKd3D3pK97C7ZzdGqk8c3RQZH\nkhyVzIj4EVyacin9evZzAlh4In0i+hAVEoVp500HHcEYQ3hwOOHB4fTr2e+c+7saXBRWF3Ks6hiH\nKg+RX5FPXnke+RX57CjcwT8P/POkcNojqAcpUSkMih7E4OjBDI4ZzODowQyIHEBws2Wu+sf0YGxS\nNO9vPcK3PRXIAoPgxj/D81fB69+E296GAWcbfSIibeG1QGatdRlj7gI+AAKBP1trtxljfgGss9a+\nDfwn0BN4zf1D96C19mpv1STS7Sx/DDa9ApkPOjOxe9DSrYcJCmhgcP9S3ty9np1FO9ldspu9JXs5\nVv3l/1+FBYYxKHoQk/pMIiUqheTI5KZHdGh0pwhcnhYUEERiRCKJEYmM6TXmlO31DfUcqzpGXkUe\n+8v2s7dkL/tK97Hx2EaW7lvatF+gCWRg1ECGxw1neOxw0uLSmJEWylMfHeNwaTV9o9vfDQpAaE+4\n5TV49lJ4+Sa4/QPoneaZY4sI4OUxZNbapcDSFu/9rNlzz/3vuoicbN2fYcV/wvjbYOYP2324alc1\nOcU57CjcwY7CHbyVt5bw1MN88x9OS06PoB4Mjh7M1H5TGRIzhCHRQxgcM5j+Pfu3qrtNvhQYEEjf\nnn3p27Mvk/pMOmlbVV2VE9JK97K3ZC+7Snax6dgmlu378p6oiGE9WfDhEr4yOIO02DRGJ4wmOTK5\nfeE3IgG+/jcnlL14PXzrHxDdv+3HE5GT+MWgfhHxsB3vwnv3wrBL4conz3uusfqGenaX7Gbz8c1s\nLtjMloIt7Cvb13Q3Ys/gKE6c6M2Fiddw3ajJpMWnMTByYLvGcEnrhAeHMzJ+JCPjT57WsfREKTnF\nOews2snvP/mYIxWHeHH7i9Q1OOtbRoVEMSZhDKMTRjc9EnoknN/JY1PgltfhL1c4d+zevgx6xHro\nm4l0bwpkIl3N3o+dsT79J8CNf3HGAJ3D8erjbC5wwtfm45vZenwr1S5nQtDY0FjG9BrDv6X8GyPi\nRjAibgQvfFrC/23dx+PzLyEuon1zmYlnRIdGM6nPJCb1mcSR3Ek8/fEePntgJiWuPLYe38qW41vY\nenwri7Ysot7WA9A3oi+jE0YzNmEsGb0zGBU/6qQxaafVdyzc/LITyF65Gb7+dwj2UNeoSDemQCbS\nleSvh8XzIH6oswROaM9TdrHWsr9sP+uPrmf90fVsPLaR/ArnBuggE8TwuOFcO/RaxvYaS3pCOkmR\nSSd1dVlrWbZ1J9MGxyuM+ak56X354/LdfLCtgNumDWd43HBuSHXWK62qq+KLoi+aAtqW41v4x4F/\nAM5draMTRjO+93jG9R5Heu90okKiTj3BoIvg+mfgtW/C699y1sBsRfAXkTPT3yCRrqJgJ7x4I4TH\nw61/a5r4tbH7cd3RdU0hrKimCID4sHjGJ47n5rSbSe+VTlpcGmFBYWc9zY7D5ew7XsmdMwZ7/StJ\n26T1iWJ4YiRvZR/itmkpJ20LDw5nfOJ4xieOb3rvePVxso9ls+HYBjYe3cift/6ZeluPwZAam0pG\n7wzG9x7PhMQJJEa4JwEedZ2z1uWy++Gd78HVf4QAjRUUaSsFMpGuoOQg/PVaCAzGdesb7DhxnHVb\n32f90fVsOLaB8tpyAPpF9GN6v+lMSJzAhMQJDIwaeN4Dvd/alE9ggGH2qI6bnV/O3zXj+vHb93eS\nW1RFclz4WfdN6JHAJQMv4ZKBzn1WVXVVbDm+pSmgvbPnHZbsXAJASlQKk/pMYnLfyUwaewPx1cWQ\n9SsIDocr/rPda6OKdFcKZCKdnC0/yr4Xr2FVcB2rh81g7Ye3UVFXATj/eF468NKmANaaObLOpr7B\n8tbGQ2Sm9iK+Z6gnyhcvuTrdCWRvbzrEd78y9Lw+Gx4czpS+U5jS15lvzNXgYmfxTtYfWc+aI2tY\num8pr+W8BsDQmKFMGZXJpG0vMjEomOhLf6VQJtIGCmQindDRyqOsrljNh1nvsHrfPzgWaYEe9K86\nzOyU2UztO5WJfSae/11057BqTyFHymr46ZyR595ZfCopNpxJKbG8uTGf72QOadeUF0EBQYyKH8Wo\n+FHcNuo2XA0uthduZ82RNaw5vIY3yjfyUmIvzOF3GLF4FZOHXcWUvlOobTjzMlcicjIFMpFOoKy2\njLVH1vL5oc9ZfWQ1+0r3ARB73DC5upqp6d9gythvkByZfI4jtc/fNuYRGRbErBG9vXoe8YyrM/rz\n0ze3suNwOSP7nWZwfhsFBQQxttdYxvYayx1j7qC2vpYtxzazJutnrCndxUvb/8pz254jiCBe+/A1\nLuh3ARf0u4DU2NRuORGwSGsokIn4IWstO4t38kneJ3yS/wmbCjbRYBvoEdSD8YnjuSHlCkZlPcP4\n8lwC5r4Mw/7N6zVVnnDx/tYjXJPRj7BgzTfWGVw5pi8/f3sbb2bnezSQtRQSGMKEvhOZcNPbLHx9\nPtVfvMuGmfewpKiI3Opcfrf+d/xu/e9I6JHABf0uYFq/aUzrO434HvFeq0mks1EgE/ETFbUVfH74\ncz7J/4RP8z5tWn5oRNwIvjX6W1zQ7wLSe6UT7KqBF66noXQ/AXNf6pAwBvDBtiNU1dZz/fikDjmf\ntF9cRAhfSevN3zbkcf/s4QQHevkuyMAguOFZeiyex/SsJ0lI/S7D5/2do5VHWXV4FZ/lf8aKvBW8\nvTib9SEAACAASURBVOdtwPmz3dh6Nq73uHPPgSbShSmQifiItZZ9pfv4JP8TPsn7hPXH1uNqcNEz\nuCfT+k1jRv8ZXNj/QnqF9/ryQycq4P+3d+fxUZX34sc/zyzZV7IvLIlJWJKwhyAxiIJKtRW0SrUW\n1GpbrdUu2tb23l/b23pv23tbb2vtrVXcFW3dqVIVF4QAsssSAiRAIAkJkASykX2e3x9PMiSIFGEm\nZyb5vl+vw5wzczLzzWFyzvc86/PXQ9Umdo77ITmjvzBg8b62pYrhw4KZOlJGZvcnN04bzvKdh3m/\n5DBzc5K8/4GOQPjK8/C3mxi958+wMZOEqbcyP2M+8zPm49IuSupLWFO1hjWH1vB08dM8vuNxgh3B\n5CfmU5haSGFKIUlhAxCrED5EEjIhBlBrVysbajawsnIlRVVF7gFZM6IyWDhuIYUphUyMn4jTdpqS\ngvYmWHIDVKyDLz9Obe2wAYu7ov4ERWW13HNpprQB8jMXZ8WTGBHEC+srBiYhA3AGwVeep+4vVxLz\n5vdAuyDvNgBsyubuIPCN8d+gpbOFDTUbWF21mlVVq1hRuQIwfxO9ydln/k0IMYhIQiaEl1U0VbCy\nciWrqlaxoXoDHa4OUxqQlM/Xc75+dqUBrcfh+eugajNc+xjkXAsrVgxI/AAvrD+IAm6Y5t1OA8Lz\n7DbFgqmp/OnDMqqOt5ISNUDTHDmD2JHzEy6uWQxv/cAkZdO+8andQp2hzBo+i1nDZ5lS48b97raT\nz+58lid3PHnmUmMhBglJyITwsI7uDjYd3uSuiixvLAdgZMRIFoxeQGFKIVMSpxBoP8txvFrq4Nn5\ncKQEFjwNY7/kveBPo6PLxd83VjB7bAJJkTJnoT9akDecP31Yxt83VPD9y7IG7HO1zWmmVXrpFlh2\nH7i6Yfodn7m/Uor0yHTSI9O5OftmWjpbTLvKngStd4qnscPGUphayMzUmeTE5Mik9mJQkIRMCA+o\naalxJ2AfV39Ma1crAbYA8hLzuGHMDVyUchEjI0Z+/jduqjEj8B/bDze+MGAN+Pt6d2cNtc0dfDV/\nxIB/tvCM1OgQCjPjeGljBffMzsRuG8BqZ0cgXP+0mfD+7R+bqveZ953V4LGhzlBmj5jN7BGz0Vqz\n59ge99/Z4u2LeXTbo0QFRlGQUkBhSiEFyQVEBUUNwC8lhOdJQibEOeh0dbL1yFZzcahaRemxUgCS\nQpO4+oKrKUwpJC8xjxDnmaesOaPjFfDMPJOU3fSSmdDZAkvWHSQ1OpiZmVJN5M++Om04dzy3mfdK\nDnNFduLAfrgjAK5/Ct74Dnz4ALTWw+X/+bnmvlRKMXqYmSj99tzbaWhvYO2htaZXclURb+17C5uy\nkRubS2GKKT0bM2yMtHkUfkMSMiHOUm1rrbvh8ZqqNTR1NuFQDiYnTObeKfdSmFpIemS6Zy4Ah3fC\nc1+GjmZY+BqMyD//9zwHu2uaWLO3jh9eMXpgS1WEx80Zm0BKVDBPrt4/8AkZgN0J8/8CwVHw8f+Z\ndpFX/8kMlXEOIgMjmZs2l7lpc3FpF8W1xaysWklRZREPf/IwD3/yMHHBce6OAdOTphMWEObhX0oI\nz5GETIjP0O3qpriu2F1FUlxXDJyciLkwtZALky70/Em+fDW8eKOZrPnWf0Jijmff/3N4vGgfQU4b\nX50m1ZX+zmG3cfOMkfzXsl0UH2ogOzly4IOw2WDubyAkBj78T2g7Dtc9aXplns/bKhu5cbnkxuVy\n18S73DdPKytXsrx8Oa+WvorD5mBK/BR3gpYWmSalZ8KnSEImRB8N7Q3uUrDVVas51n4Mm7IxPnY8\nd0+6m8KUQu9Wg+xcCq/cDtEj4WuvQJR1idCRpjZe33KIBXmpRIcGWBaH8JyvTB3BH94r5Ymicn6/\nYII1QSgFF/8IgqNNQ/9n5sENSyDUc6P2xwbHMi9jHvMy5rmbF6ysWsmqylX8buPv+N3G35ESluKu\n2sxLzCPIcX5JoRDnSxIyMaT1naJoZeVKttVuw6VdRAdGuxsKz0ieMTANhTcshrfug9Q8+OrfIGTg\nxhk7nefWHqDT5eLrBWmWxiE8JzLEyXVTUnlxfQU//sJo4sMtTEKmfcOUlL12Bzw+B256GWIu8PjH\nOG1OpiZOZWriVH4w5Qccaj5EUVURqypX8cbeN3hx94sE2gOZljiNmakzKUwtJCUsxeNxCPGvSEIm\nhpymjiZ3V/qiqiKOth4FIDsmm2+O/yaFKYVkx2QPXFd6Vze8+++mXU3WF+C6JyDgPDoDeEBrRzfP\nfnyA2WMSSI+TdjeDya0FaTz38QEeL9rPT74w1tpgcq6FiGR44UZYPMeUlI280KsfmRyWzILRC1gw\negHt3e1srNnIysqV7rECWQcXRF7grtqclDBJBqUVA0ISMjHo9XaXL6oqMhN1H9lKl+4i3BluBptM\nNYNNxgbHDnxwbQ3w8m1Qthzy7zA9z86xkbMnPb/uAMdOdPLNmelWhyI8LC02lC+OT+a5tQe4Y+YF\n1ldHj5gOt78HSxbAM1ebhv+51w3IRwfaAylIKaAgpYD7p93PgcYD7sTsuZLneKr4KRmUVgwY68/8\nQnhB70TdvUnYkRNmou4xw8ZwS84tXJRyERPiJuCwWfgnUL/PTIVUvxe++AeYeqt1sfTR2tHNIx/t\nY8YFMUxLs7baVHjHXZdksHTrIZ5cvZ8fXD7a6nBMVeVty+HFm+CV28wgyJf8FAZwwFelFKMiRzEq\nchSLshedcVDa3qpNGZRWeJIkZGJQ0FpTdrzMPSbRlsNb6NL9J+ouSCkgPiTe6lCN8iL420JAm2Et\nPucYY7lP55qVp2H7zds9GtqS9QepbW7nz1+ddP5v9os+Pfl+0XD+7weMuv8t93r5b67yyHt6g9fi\n9MAxHZ0YzhXZCTy5ppzbZ6YTEeT5KrnP/R0NGQaLXoe37oVVv4PqrfDlx0zjfwt81qC0KytX8tj2\nx/jrtr/2a2takFJAZKAFPVfFoCEJmfBbfe9gi6qKOHziMABZ0Vksyl5EYUohE+In+Fb7D61hzUPw\n3n+YUoEbX/RKQ+Zz1dbZzSMf7WV6+jDy0z3X6034nrsvzeSd4sMsXrWfHwzgdEpn5Ag0Y5MlT4J/\n/hgevcS0K0sYZ2lYpxuUtrc3dlFVEW/uexObsjEhboK752ZWdJYMqyE+F0nIhN/odnWzq34Xaw6t\nYW31WrYc2UKXq4tQZygXJl3InSl3UpBSQGKoBYNeno3W4/DGXbDrTRg3D65+GIIirI6qnydXl3O0\nqZ0/3eiB0jHh03JSIrkyN5HFq/bxtekjrO1x2ZdSkHcbJOTA3xeaxv7zHjYdAHxEZGAkV6ZfyZXp\nV9Lt6mZH3Q53T+2HtjzEQ1seIjY4lulJ05mRPIMLky+0po2q8CuSkAmfVt1czdrqtaw5tIZ11es4\n3n4cMG3BFo5bSGFKIRPjJuK0+1Ap2OnUbDdVlA0VZmDM/DvOai6/gVTX3M7/fVjG7DHxTJfSsSHh\nh1eM4d3iw/zxvVL+85pcq8Ppb0Q+fPMj+PsiMw/m/pUw99fg9K0J7u02OxPiJjAhbgLfmfQdjp44\nSlFVEWur17K6ajVv7nsTgMzoTGYkzWBG8gwmJ0yWcc/Ep0hCJnxKS2cLG2o2sPaQScLKG8sBiAuO\nY2bqTGYkzyA/Kd9/7jZdLlj/V1j+c9NG5pZllk2D9K889H4pJzq7+cmVY6wORQyQtNhQbpw2giXr\nD/L1i9K4wNeGOIlIglveMvNfrv4jVKwzw8LEWzxcxxnEhcRxTeY1XJN5DS7tcpfqf3zoY5bsWsLT\nO58mwBbA5ITJzEg2CZpUbwqQhExYrMvVxc66naw9tJa11WvdQ1IE2YOYmjiV67OuZ0byDC6IusD/\nTlhNNfD6nbD3A8iaa6oow3yzy3zZkWaeX3eQG6cNJyM+3OpwxAC6Z3Ymr26u5IE3d/LELXm+93fm\nCIDLfmk6vrx2h2lXNvfXMOUWnytlPpVN2RgXM45xMeO4Pfd2TnSeYNPhTSZBq/6YBzc9yIObHiQm\nKIbpyaZ6c3rSdN/pfCQGlCRkYkC5tIvd9btZX7Oe9TXr2Xx4M82dzYDpTr4oexEzkmcwKX4SAXY/\nnq6n5E1Yejd0tsJVD8LUr/vsxUNrzf97fQfBAXa+O9tHGneLARMXHsj3L8vigbdKeKf4MHNzfLQN\nZsYcuGM1vPYtePN7sHsZfOmPZmBZPxHiDDEDzqYWAnC45TBrq9eaG9JDa3lrn+mZOypiFHmJeUxL\nnMbUxKn+UyMgzoskZMKreoej+KjxI1774DU2Ht5IY0cjACMjRjI3bS7TEqeRn5TPsKBBMOZVSx28\nfT9s/zskTYBrF0Ocbyc5r26uYu2+Oh6Yn0NceKDV4QgL3DJjFC9vquSX/yimMDOW0EAfvTSEJ8DX\nXoUNj5lmAP83Hb7w3zD+Kz57w3MmCaEJzM+Yz/yM+Z+6WV22fxkv7XkJMDMH5CXmkZ+UT3t3u8VR\nC2/x0b864a+01pQ3lrOhZgPrqtex8fBG6tvqAUjpTGH2iNnuO7+E0ASLo/UgrWHHK/DPH0FbI1z8\nYyi8z1S3+LD6lg4eeGsnk0ZE8dVp1k1kLqzlsNt4YH4O1z2ylv9dvod//6K1w0yckc0G+d8yJWav\nf9uUmO18A676vV+Vlp3KpmyMjRnL2Jix3Jx9s7s5x/qa9Wyo2eCed1OheHLpk+7z6JTEKUQE+FZv\nbXFuJCET56XL1cXu+t1sPrKZzYc3s/nIZncClhCSQEFyAXmJebgOuPjynC9bHK2XHK+AZffBnrch\nZYppK2bxuElnQ2vNz5cW09TWxa+vzcVm878SBuE5U0cN46b8ETy+ej9zxiX4fk/bmAvg1mWw7hF4\n/5fwcB7M+onpwewD04+dL4fNwfi48YyPG8/tubfT2d3Jjrod/G3N36gNrOWlPS/xXMlz2JSNrOgs\nJsVPYnLCZCbHT5Y2aH7K/7+1YkCd6DzB9trt7uRr69GttHa1ApASlkJBcgGTEyaTl5jHiPAR7gbC\nK6pWWBi1l3S2wuqHoOh/zfYV/2UuBn4ylcrrn1Txj62HuO/yLMYkyh22gJ9eOZaislrue2kr//xu\nIeFeGMHfo2x2uPAuGH2lKZ1+999g6wum3aaP9mY+V067k0nxk2iIamDWrFm0d7ez7eg2NtRsYPOR\nzbxe9jov7HoBMOfiKQlTTJIWP5m0yDTf66whPkUSMnFGR08cZdvRbWw+spktR7ZQUldCl+5CociK\nzmJ+xnwmx09mUvykwVUFeSZam8Fd3/kpHD8I4+bD5Q9A1HCrIztrFfUn+H+vF5M3Kpo7Z2VYHY7w\nEaGBDh5cMJHrH1nDz5cW8/vrJ/jHhXxYGnz17+bv8p8/hicuhwk3wqX/DpGpVkfnFYH2QPIS88hL\nzAOg09VpaisOm3N1UVURS/cuBSAqMMqdnE2Mn8i4mHH+3WlqkJKETLi1dbVRUl/CtqPb2HZ0G9tr\nt1PdUg1AgC2A3Lhcbs25lckJk5kQN4HwgCE4PELlJnjv51C+CuLGwqKlkH6x1VF9Lm2d3dy1ZDMK\neHDBROxSVSn6mDIymrsvzeSP75cyZWQ0N+WPtDqks6MUjP0SpF8CK/8HPv4LFL8G078NF33f52bF\n8DSnzUlObA45sTksyl6E1poDjQfYcmSLu0nJhxUfAqY6dOywseTG5pIbl8v42PEMDx/uH8n3ICYJ\n2RDl0i4ONB5ge+12dwJWeqyULt0FmCLvCXETWDhuIbmxuXJHdXQ3fPArKPkHhMSanl1Tb/O7tipa\na3762na2VTbw6MIpDB8WYnVIwgfdMzuTTyqO84ulxYxLimDSCGsm+D4ngWFw2X+Y6Zfe/xUUPQib\nn4GZPzRjlzmHxgj5SilGRY5iVOQorsm8BoDa1lo+OfIJ22q3sf3odl4re40lu5YAphQtJzaH8bHj\nyY3LJTc2VyZLH2D+dTUR58SlXVQ2VbKzficldSWU1JWwo24HTR1NAIQ6Q8mJzeHWnFvdd0wy7k2P\n2jJzQt/6AjhDYdZP4cJvQ6B/lg4+XrSfVzdX8b05mVye7aPjTQnL2W2KP94wkS89XMS3nt3Eq9+e\nQWq0nyXvUSPgy4/B9Dth+c/g7R/D6j9Awfdgys0+NwXTQIgNjmXOyDnMGTkHMJ2y9h7f607Qttdu\nZ3XVajQaMOOhZcdmM3bYWMYOG8uYmDHSo9OLJCEbZLpd3ZQ3lrOzbicl9Sb52lW/yz34qsPmIDMq\nk8tHXs6EuAnkxuaSFpmG3U8aog+Y6q2w6kHTnd4RCPl3QuG9EOrjPc/O4PUtVTzwVglzsxO559JM\nq8MRPi4qJIDFi/K4/pE1LHpiPa/cMYPoUD8sJU+ZDDf/wzQzWPEbk5gV/S8U3AOTF/ntzZUnOGwO\nRg8bzehho7k+63oAmjuaKa4rdteebKzZ6B6wFiA1LJWxMWMZFzPOJGnDxhAT7L/nRV8iCZkfa+po\noux4GXvq91B6vJTd9bvZfWy3u9djoD2Q0dGjuSr9KvcfT0ZUhu9PxG0Vl8tMc7TuL1D2HgRGQOEP\nTDLmo1Mena0Pdx3hvpe2Mj19GH+4YaIMcSHOyujEcB5bNJWFT6zn1qc28Mxt04jw9Z6Xp6OUmXop\nbSbsXwUf/dZ0ylnxW5i80IxrFiXj8AGEBYSRn5RPftLJXqp1rXXsqt9FSX0JO+t2sqt+F8sPLHe/\nHh8Sz7hh4xgTM4bMqEwyozMZET5CbvQ/J0nI/ECnq5PyhnL2HNtD6bFSSo+XUnqs1N3gHiDMGUZm\ndCbXZl7L2GHm7iUtMg2HTf6L/6XW4/DJEjP6d/0+CI2H2T+DvNshyP/bULxTXMPdS7YwJslcXIOc\ncpIUZy8/PYY/3TiJu57fzMLF63j669OICvHDkrJeaYVmqdwIa/9sGv9//BfTISD/WzDiQr8c9d+b\nYoJjKEgpoCClwP1cY0cju+t396uN+ajyI3d1Z6A9kPTIdDKjM91JWmZ0JnHBcdJ54DPI1dqHtHa1\ncrDxIPsb9ruXsoYy9jfsp8tlGts7lINRkaOYGD+RBdEL3F/0pNAk+ZJ/HlrDwY9h6xLY/jJ0noDh\n+XDJv8HYq31+hP2z9ermSn748jZyUyJ56tY83x9XSvikK7ITeeRrU/j285u58bF1PHlLHomRft44\nPnUqXP+kGdh5/aOw6WnY+TrEZMCkhWbYjPAhMpTPOYgIiOg37AaYa9i+hn2UHiul7FgZpcdLWXto\nrXv4DYDIwEgyojLIiMogLTKNtMg00iPTiQ+Jx6ZsVvwqPkMSsgGmtaaura5f0rW/cT/lDeUcaj7k\nvrtQKJLDkkmPTKcwpZDM6EyyorNIi0iTKsfzUb8ftv3NNNI/Vm4a6mdfC9O+AckTrY7OY1wuze+X\n7+bPH+5lxgUxPLpoKmG+Oj+h8AtzxiWw+Oap3PncJq5+uIjFN09lfGqU1WGdv6jhcPmvYNb9UPw6\nbHnWDG3z/i8hay6Mvx4yr4AAP+vUYIFgRzDZMdlkx2T3e/5423F3zU7Z8TJKj5WybN8ymjqb+v3s\nqIhRjIoYRVpkGqMizePIiJEEO4ZGBww5Q3tBt6ubwycOU9FU0W+pbKqkoqnC3cAeTn4JJ8RNYH7G\nfPcdw4jwEQQ5/PwO1FfU7YWSpWbIiqpNgDJVFhffb6opAsOsjtCj6prb+eHL2/hg1xFuyBvOf8zL\nJtAh1ZTi/M3MiuOVb8/gtqc2suCva/n5l7K5IW+QjF8VEAqTbjLL0T0mMdv6Iux+C5whJjnLudbM\noTkEe2iej6igqE+Vpp1aOFHeWM7+hv1sq93G2+VvuwsnAJJCkxgRPoLU8FRSw1MZHj7c/TiYen1K\nQnYOtNYcbz9OdUs11S3VHGo+1C/pqmquotPV6d7fYXOQEpZCangqE+ImuDN/Kab1ku4uOLTZNMwv\n+Qcc2WmeT55k2oblLvCrUfU/jw92HeZHL2+nsbWTX83L5mvTRw6Oi6XwGWMSI3jjOwV8/2+f8JNX\nt/PR7qP8an4OceGBVofmOXFZptRszi+gvMgMMFuyFIpfNclZ+izIvAwyLhu05xJvU0oRGxxLbHBs\nv0QNoL27nQONByhvKHfXIlU0VfBhxYfuuZJ7RQZGkhrWP0lLCUshOTSZhNAEvxo/UxKy0+jUnVQ0\nVrgTruqWampaavqt9/Zk7BXqDGV4+HAyozO5ZMQlDA8f7l4SQxKlt4k3aQ3HD8DeD2Hv+7BvJbQ3\ngLKZBrpzfwNjrhrUvagq6k/wX8tK+OeOGsYkhvPsbdMYmzR47hyFb4kNC+TpW6fxeNF+/vudXaz+\nfS0/vGI0N+WPHFwzP9jsZiaO9Ivhyt9B+UrY9RbseRd2LzP7xI8zpWajCmHE9EE/I8BACLQHkhWd\nRVZ01qdea+lsobKp0l3jVNFUQWVzJcV1xbx34D334Oa9YoNjSQpNIjE0kaTQJPeSGGa2tdaf+gyr\nSEJ2iuUHlnPvwXvRB/v/J8UExZAUmkRGVAYXpVxEcmhyv//U6MBoKYkYKN1dULMNKtaZhvkV66Hp\nkHktIhWy58EFl0LaxRAyzNpYB8Bv397FE0X7sSnFvZdl8c2L06WKUnidzab4xsx0LhkTz8+X7uBn\nbxSzZN1B7pmdydzBOOiw3WHOKxdcCldqqN0Dpe/CnndML801D5mbwMTxMOoiczOYMgUikqyOfFAJ\ndYa6x047VZeri5qWGqqaq/oXpjRXU3qslFWVq2jrbuv3M1dFXsUlXDJQ4Z+RJGSnyIzKZG7kXC7M\nvpCksCR3sWegfRAVx/uTrnY4UgI1208u1Z+YXpEAkcNh5AxzZ5p2McRmDrku6498tJcvjU/m/i+M\nITlK2raIgZURH8Zzt+WzbHsNv393N99+fjOjE8JhMN8LKQVxo80y427oOAGV6+HAGihfDesfg7UP\nm33Dk0xzieTJ5jExF8Lih9x5aiA4bA53O7PTObW5UU1LDV0Hu067rxUkITvFqMhRXBl1JbMyZ1kd\nytDS1gj1e81URXVlUFdq5o88ugt6hvzAGQqJOaZL+oh8GD4dIlOsjXsA1Ta3897Ow7y0qRL6dPha\n/v2LyYgfXB0ThH9RSnHV+CTm5iTy5rZD/PnDsn6vF5XWkp8+DKd9kLaXDehpV5Y+y2x3tpkbx0Nb\nzFK1+WQVJ0BQFMSP7Unqeh5jMiAi2VSTCq9QShEdFE10UDTjYsYBsOLwCmuD6sOrCZlSai7wR8AO\nLNZa/+aU1wOBZ4ApQB3wFa11uTdjEhbQGkdnE1Rvg8YqaKg0S2MVNFSZRKz5cJ8fUKa9V2wWZF4O\nSeNNNUB0GtgG6Qn9NE50dLG1ooGN5fV8sPsIn1QcR2tTItE3IZNkTPgKu00xb2IKV09IZvwzJ5//\n2uPriAx2Mmt0HNPTY5iWNoz02NDB28zDGWRK7UdMP/lcW4OZku3wTnOjeXSXGWaj7amT+9icppNA\n1EiIHgXRI00tQHgShCeaRQxaXkvIlFJ24M/AZUAlsEEptVRrvbPPbrcBx7TWGUqpG4DfAl/xVkzC\nA1wu6GgyJVrtTdDeaNZP1EHLUbO412t7lqNc1NUKq/u8j81p7gYjU01PpdgMc4cYk2ESL+fQGfKj\no8tFTUMbZUebKDvSTNmRZnZWN1JS3US3y7RlnJAayffnZHHpmHiykyP6XeyE8DWnJlqPLpzC2ztq\nWFlayxufmPaeMaEBjEuOYHRCOFmJ4WQlhJMaHUxMaMDgTNSCIk9O39RLa2g+YpKzY/vN2IjHyuHY\nATOPbmv9p97mInsI7EiFsASToAUPg+Bo017WvR5tHoOjISDctH8TPs+b/0vTgDKt9T4ApdSLwDyg\nb0I2D/hFz/rLwMNKKaV9qdvDQNDaLJzp0WWq7lzd5rG7s2e7z3OuzlO2e/fr83pXO3S1mSL1rlaz\n3dlqnjvd8x3NJvHqTcA6ms78u9gDIDQOQmLMY2wmhMZRduQEGZMvNnd7kSlmeiI/Lu3SWtPZreno\ndtHZ5aKj20VHn8fObhftXS6a2jppbO0yj21dNLZ10tjaydGmdmoa26hpaKO2uaPfe8eGBZCVEM6d\nF1/AlJHRTBoR5d9T1Ygh7/LsRC7PTkRrzf7aFtbvr2fjgWPsqmnk2Y8P0N7lcu8b4LCREhVMUmQQ\n0aEBRIc4iQ4JICrErIcEOAgOsBPs7FkCbAQ57QQ57ThtNmw2cNhs2G0Kh0359rytSpnZAMITgIs/\n/Xpbo6lNaK6BJrPU7NpIaoTd1CpUboATx0yv8jOxB5rxFgNCTYIWENpnO8wM5eEINIs98OS6ezvI\nzF7S+5rdCTaHWZTt5LrNfvJR2U95vmdb9ayjetrR9TwOxiT8c/JmQpYCVPTZrgTyP2sfrXWXUqoB\niAFqvRjXGW1b8TLjVtxH7QqzrdDupf820GfdvH5y/XT7n7qPDd/IOzux004A7QTQRgAdOHu2nZwg\nmGYiaSKJFoJpJoRmQmgihBaC3Y/1RHBMR9DSFQwNCnrOD72/YVdXF44yB1CL1kf7ff7pjsLpUnJ9\nmj1Pv9/p3tCz79dbcvV5BThsRAQ5iA0LJDEyiNyUSBIigkiODCY9LpSM+DBJvsSgpZQiPS6M9Lgw\nbphmhqHpdmkO1LWw92gLh463UtWzVB9vZeehRo6d6KChtfO0f5tn95mYxEyZBM1uU+4SuN4cQHGy\nVE/1+bnerb779W6r07zm3ZK9RCCRtrYxBNX1qUFQYA/sJpxmInQzETQRoZuIpIlw3UIIrQTrNkLa\nWwluayOEVkJoI0QfJ5hWQnQbgbQTQCcBdOLEukburtNePXFfLU+9+rpOc3U9dfksva81xVwLs2Z5\n9fc6W35RjqmU+ibwTYCEhARWrFjhtc9qrD5GrXMCymbr9x/NKV8ErU5NyfqkWurk/qd+sU59H/f7\nq9M/r3vuIFwourHjUnZc2OnGhkvZzXPY6VZ2XNhwYadL2fu8ZqNbOejGhlZ2OnHSoQLoVD1/5ns5\nfAAACANJREFUfsqJS/VvRHq6r/CZzjMhPUvqZ/0s0NGpCXD2eUZ9ep/T/+S/juNsT4Gf9/c608+a\nkzw4bQqHDRx9tu02cPasBzshxKEIdiiCHRBg730nF3CiZwFaoLkFPik/y1+mD2/+PZyvWX3WvRGn\nJ9+zubnZa8fSk+87y0vv601nE6cTGAmM7D2hJPe+EoBLOznRCc2dmvZuTUc3ZnFp2ruho+c5l4Zu\nDS6tcem+2z2PLk23hlNvx3Tvv/rktu7/onu738/12Rio2+vOABdOZ+dpXjEHroV4WoDqc3x/pV04\n6MKpO3HSiaPn0dnn0U43Nu3CRnfv1Qibdl+ZsOue53qvVj3bPVckbNp1hqtjn0IQfTLVOpmSnVq4\n4TLnZ93/avzpAo+T26rPeqtzmM/8HXkzIasC+g5hnNrz3On2qVRKOYBITOP+frTWjwKPAkydOlXP\n8mo2O4sVKzLx7mcMPStWrJBj6klPn1z16eO64uSqx+J8+y3Pvyde+I56KU6vHFNv8JfvqJ+Rc6ln\n+dLx9GYjng1AplIqTSkVANwALD1ln6XAzT3r1wEfDLn2Y0IIIYQY8rxWQtbTJuw7wDuYYS+e0FoX\nK6V+CWzUWi8FHgeeVUqVAfWYpE0IIYQQYkjxahsyrfUyYNkpz/2sz3obcL03YxBCCCGE8HX+O+6A\nEEIIIcQgIQmZEEIIIYTFJCETQgghhLCYJGRCCCGEEBaThEwIIYQQwmKSkAkhhBBCWEwSMiGEEEII\ni0lCJoQQQghhMUnIhBBCCCEsJgmZEEIIIYTFJCETQgghhLCYV+eyFEJ4x/abt7NixQpmzZpldShn\n9osGj79l+W+u8vh7eoPX4vTCMfUGv/mOCuEjpIRMCCGEEMJikpAJIYQQQlhMEjIhhBBCCItJQiaE\nEEIIYTFJyIQQQgghLCYJmRBCCCGExSQhE0IIIYSwmCRkQgghhBAWk4RMCCGEEMJikpAJIYQQQlhM\naa2tjuFzUUodBQ54+WNigVovf8ZQI8fU8+SYepYcT8+TY+p5ckw9ayCO50itddy/2snvErKBoJTa\nqLWeanUcg4kcU8+TY+pZcjw9T46p58kx9SxfOp5SZSmEEEIIYTFJyIQQQgghLCYJ2ek9anUAg5Ac\nU8+TY+pZcjw9T46p58kx9SyfOZ7ShkwIIYQQwmJSQiaEEEIIYTFJyD6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220 | "text/plain": [ 221 | "" 222 | ] 223 | }, 224 | "metadata": {}, 225 | "output_type": "display_data" 226 | } 227 | ], 228 | "source": [ 229 | "plt.show() # Show the figure right here." 230 | ] 231 | }, 232 | { 233 | "cell_type": "code", 234 | "execution_count": null, 235 | "metadata": { 236 | "collapsed": true 237 | }, 238 | "outputs": [], 239 | "source": [] 240 | } 241 | ], 242 | "metadata": { 243 | "kernelspec": { 244 | "display_name": "Python 2", 245 | "language": "python", 246 | "name": "python2" 247 | }, 248 | "language_info": { 249 | "codemirror_mode": { 250 | "name": "ipython", 251 | "version": 2 252 | }, 253 | "file_extension": ".py", 254 | "mimetype": "text/x-python", 255 | "name": "python", 256 | "nbconvert_exporter": "python", 257 | "pygments_lexer": "ipython2", 258 | "version": "2.7.13" 259 | } 260 | }, 261 | "nbformat": 4, 262 | "nbformat_minor": 2 263 | } 264 | -------------------------------------------------------------------------------- /Homework_1_problem2.2.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "markdown", 5 | "metadata": {}, 6 | "source": [ 7 | "# Homework 1 Problem 2.2\n", 8 | "We import sympy and pyplot. For this problem we will also need $|x|$, so we need to get the complex number absolute value. Looking up in the sympy documentation, this is in sympy.functions.Abs(), so we need to import that, or else type functions.Abs() each time. We do the same for the complex conjugate, which is just conjugate().\n", 9 | "We also want to look up what the complex number $i$ is for sympy, but that is simply I." 10 | ] 11 | }, 12 | { 13 | "cell_type": "code", 14 | "execution_count": 1, 15 | "metadata": { 16 | "collapsed": true 17 | }, 18 | "outputs": [], 19 | "source": [ 20 | "from sympy import *\n", 21 | "from sympy.functions import Abs, conjugate\n", 22 | "import matplotlib.pyplot as plt" 23 | ] 24 | }, 25 | { 26 | "cell_type": "markdown", 27 | "metadata": {}, 28 | "source": [ 29 | "We want to define $\\Psi$ as a function so we can use it in multiple parts of the problem. As usual, we also define variables we need." 30 | ] 31 | }, 32 | { 33 | "cell_type": "code", 34 | "execution_count": 2, 35 | "metadata": {}, 36 | "outputs": [ 37 | { 38 | "data": { 39 | "text/plain": [ 40 | "A**2*exp(-2*lam*Abs(x))" 41 | ] 42 | }, 43 | "execution_count": 2, 44 | "metadata": {}, 45 | "output_type": "execute_result" 46 | } 47 | ], 48 | "source": [ 49 | "A, lam, x, om, t = symbols(\"A lam x om t\",real=True)\n", 50 | "assumptions.assume.global_assumptions.add(Q.positive(lam))\n", 51 | "psi = Function('psi')(x)\n", 52 | "psi = A*exp(-lam*Abs(x) - I*om*t)\n", 53 | "simplify(conjugate(psi)*psi)" 54 | ] 55 | }, 56 | { 57 | "cell_type": "markdown", 58 | "metadata": {}, 59 | "source": [ 60 | "We can now get the normalization factor:" 61 | ] 62 | }, 63 | { 64 | "cell_type": "code", 65 | "execution_count": 3, 66 | "metadata": {}, 67 | "outputs": [ 68 | { 69 | "data": { 70 | "text/plain": [ 71 | "Piecewise((A**2/lam, Abs(periodic_argument(lam, oo)) < pi/2), (Integral(A**2*exp(-lam*Abs(x) - I*om*t)*exp(-lam*Abs(x) + I*om*t), (x, -oo, oo)), True))" 72 | ] 73 | }, 74 | "execution_count": 3, 75 | "metadata": {}, 76 | "output_type": "execute_result" 77 | } 78 | ], 79 | "source": [ 80 | "integrate(conjugate(psi)*psi,(x,-oo,oo))" 81 | ] 82 | }, 83 | { 84 | "cell_type": "markdown", 85 | "metadata": {}, 86 | "source": [ 87 | "So the equation to normalize the wave function is:\n", 88 | "$$ \\frac{A^2}{\\lambda}=1 \\Rightarrow A = \\sqrt{\\lambda}$$, since we can freely choose the positive root. Note that it does not make a difference if you choose any other root, including complex ones. Since you always end up squaring the wave function, any complex phase will drop out." 89 | ] 90 | }, 91 | { 92 | "cell_type": "code", 93 | "execution_count": 4, 94 | "metadata": { 95 | "collapsed": true 96 | }, 97 | "outputs": [], 98 | "source": [ 99 | "psi = sqrt(lam)*exp(-lam*Abs(x) - I*om*t)" 100 | ] 101 | }, 102 | { 103 | "cell_type": "markdown", 104 | "metadata": {}, 105 | "source": [ 106 | "We can now do the rest of the homework. \n", 107 | "$$\\left< x \\right> = \\int_{-\\infty}^\\infty \\Psi^* x \\Psi dx$$\n", 108 | "$$\\left< x^2 \\right> = \\int_{-\\infty}^\\infty \\Psi^* x^2 \\Psi dx$$\n" 109 | ] 110 | }, 111 | { 112 | "cell_type": "code", 113 | "execution_count": 5, 114 | "metadata": {}, 115 | "outputs": [ 116 | { 117 | "name": "stdout", 118 | "output_type": "stream", 119 | "text": [ 120 | "Piecewise((0, Abs(periodic_argument(lam, oo)) < pi/2), (Integral(sqrt(lam)*x*exp(-lam*Abs(x) - I*om*t)*exp(-lam*Abs(x) + I*om*t)*conjugate(sqrt(lam)), (x, -oo, oo)), True))\n", 121 | "Piecewise((conjugate(sqrt(lam))/(2*lam**(5/2)), Abs(periodic_argument(lam, oo)) < pi/2), (Integral(sqrt(lam)*x**2*exp(-lam*Abs(x) - I*om*t)*exp(-lam*Abs(x) + I*om*t)*conjugate(sqrt(lam)), (x, -oo, oo)), True))\n" 122 | ] 123 | } 124 | ], 125 | "source": [ 126 | "print integrate(conjugate(psi)*x*psi,(x,-oo,oo))\n", 127 | "print integrate(conjugate(psi)*x*x*psi,(x,-oo,oo))" 128 | ] 129 | }, 130 | { 131 | "cell_type": "markdown", 132 | "metadata": {}, 133 | "source": [ 134 | "So the first integral is zero, which was to be expected for an odd function integrated over even bounds. The second integral gives a more simplified answer if we first compute $\\Psi^* \\Psi$, and then integrate, though you can easily simplify the expression found above." 135 | ] 136 | }, 137 | { 138 | "cell_type": "code", 139 | "execution_count": 6, 140 | "metadata": {}, 141 | "outputs": [ 142 | { 143 | "data": { 144 | "text/plain": [ 145 | "Piecewise((1/(2*lam**2), Abs(periodic_argument(lam, oo)) < pi/2), (Integral(lam*x**2*exp(-2*lam*Abs(x)), (x, -oo, oo)), True))" 146 | ] 147 | }, 148 | "execution_count": 6, 149 | "metadata": {}, 150 | "output_type": "execute_result" 151 | } 152 | ], 153 | "source": [ 154 | "integrate(x*x*lam*exp(-2*lam*Abs(x)),(x,-oo,oo))" 155 | ] 156 | }, 157 | { 158 | "cell_type": "markdown", 159 | "metadata": {}, 160 | "source": [ 161 | "The results are $\\left< x \\right> = 0$ and $\\left< x^2 \\right> = \\frac{1}{2\\lambda^2}$, and so $\\sigma^2 = \\frac{1}{2\\lambda^2} - 0 \\Rightarrow \\sigma = \\frac{1}{\\sqrt{2}\\lambda}$\n", 162 | "\n", 163 | "Now sketch the function. Choose $t=0$, invert our previous answer to get $\\lambda = \\frac{1}{\\sqrt{2}\\sigma}$" 164 | ] 165 | }, 166 | { 167 | "cell_type": "code", 168 | "execution_count": 7, 169 | "metadata": { 170 | "collapsed": true 171 | }, 172 | "outputs": [], 173 | "source": [ 174 | "import numpy as np\n", 175 | "def psi_f(x,sig):\n", 176 | " return( np.sqrt(1/(np.sqrt(2)*sig))*np.exp(-np.abs(x)/(np.sqrt(2)*sig)))" 177 | ] 178 | }, 179 | { 180 | "cell_type": "markdown", 181 | "metadata": {}, 182 | "source": [ 183 | "We can now evaluate the function and make our plot. We can plot a number of different sigmas on the same graph so you get a sense of how changing sigma changes the curve." 184 | ] 185 | }, 186 | { 187 | "cell_type": "code", 188 | "execution_count": 8, 189 | "metadata": { 190 | "collapsed": true 191 | }, 192 | "outputs": [], 193 | "source": [ 194 | "x_r = np.arange(-5,5,0.01) # Set the range in x, with a small step size." 195 | ] 196 | }, 197 | { 198 | "cell_type": "code", 199 | "execution_count": 9, 200 | "metadata": { 201 | "collapsed": true 202 | }, 203 | "outputs": [], 204 | "source": [ 205 | "plt.figure(figsize=(10,5))\n", 206 | "x_ave=0\n", 207 | "for s in [0.5,1,2]:\n", 208 | " p=plt.plot(x_r,psi_f(x_r,s),label=\"sigma={}\".format(s))\n", 209 | " x1 = x_ave-s # Draw lines\n", 210 | " x2 = x_ave-s\n", 211 | " plt.plot([x1, x2], [-0.05, 0.1],color=p[0].get_color(), linestyle='-', linewidth=3)\n", 212 | " x1 = x_ave+s\n", 213 | " x2 = x_ave+s\n", 214 | " plt.plot([x1, x2], [-0.05, 0.1],color=p[0].get_color(), linestyle='-', linewidth=3)\n", 215 | " plt.legend() \n", 216 | " plt.title(\"Graph of the wavefunction for t=0\")\n", 217 | " plt.xlabel(\"x\")\n", 218 | " plt.ylabel(\"y\")\n", 219 | " plt.grid(True,which='both')" 220 | ] 221 | }, 222 | { 223 | "cell_type": "code", 224 | "execution_count": 10, 225 | "metadata": { 226 | "collapsed": true 227 | }, 228 | "outputs": [], 229 | "source": [ 230 | "plt.savefig('Homework_1p2_2.pdf',format='pdf') # Save the figure to a file, so you can print it separately." 231 | ] 232 | }, 233 | { 234 | "cell_type": "code", 235 | "execution_count": 11, 236 | "metadata": {}, 237 | "outputs": [ 238 | { 239 | "data": { 240 | "image/png": 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LIYQ1SEImhKiRdp66SFM/9wqv0H+tFvU9cXdxlIRMCGFVkpAJIWqkuPhUOgZZ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\nA6UUMzIjyEoN5T9f5fPvlQeZ+exaZg2I4P5pySSH9byZMM6Jydw5WnP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241 | "text/plain": [ 242 | "" 243 | ] 244 | }, 245 | "metadata": {}, 246 | "output_type": "display_data" 247 | } 248 | ], 249 | "source": [ 250 | "plt.show()" 251 | ] 252 | } 253 | ], 254 | "metadata": { 255 | "kernelspec": { 256 | "display_name": "Python 2", 257 | "language": "python", 258 | "name": "python2" 259 | }, 260 | "language_info": { 261 | "codemirror_mode": { 262 | "name": "ipython", 263 | "version": 2 264 | }, 265 | "file_extension": ".py", 266 | "mimetype": "text/x-python", 267 | "name": "python", 268 | "nbconvert_exporter": "python", 269 | "pygments_lexer": "ipython2", 270 | "version": "2.7.13" 271 | } 272 | }, 273 | "nbformat": 4, 274 | "nbformat_minor": 2 275 | } 276 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # QMPython 2 | Quantum Mechanics and Schrodinger Equation Solvers in Python. 3 | 4 | The starting point for these calculations is the notebook "Solving_the_Schrodinger_Equation_Numerically.ipynb". 5 | In this notebook you will find an explanation on how to setup the Hamiltonian 6 | for an infinite square well. It is very easy to change this to any shape potential, 7 | bounded on some domain [xlow,xhigh]. 8 | 9 | An example usage of this way of solving the Schrodinger equation in this way can 10 | be found in Harmonic Oscillator.ipynb, which shows how a harmonic state of 11 | the H.O. evolves over time. This problem is exactly solvable using the algebra of 12 | ladder operators, and agrees with the numerical solution here. You can play some 13 | games with this notebook, for example by adding a spike in the center of the well. 14 | 15 | A different solution, solving the Time Dependent Schrodinger Equation directly 16 | is found in TimePropagation_of_WF.ipynb. This still uses the Hamiltonian, but 17 | now solves the time dependence directly, stepping in time. This makes for good 18 | solutions to scattering problems. 19 | 20 | ## Content 21 | 22 | - [Solving_the_Schrodinger_Equation_Numerically.ipynb](https://github.com/mholtrop/QMPython/blob/master/Solving_the_Schrodinger_Equation_Numerically.ipynb) 23 | - [Harmonic Oscillator.ipynb](https://github.com/mholtrop/QMPython/blob/master/Harmonic%20Oscillator.ipynb) 24 | - [TimePropagation_of_WF.ipynb](https://github.com/mholtrop/QMPython/blob/master/TimePropagation_of_WF.ipynb) 25 | --------------------------------------------------------------------------------