{ "cells": [ { "cell_type": "code", "execution_count": 8, "id": "c02429b3", "metadata": {}, "outputs": [], "source": [ "# first I import the needed libraries\n", "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 9, "id": "95fcbb52", "metadata": {}, "outputs": [], "source": [ "#decide on a value for L\n", "L=2\n", "# create an array of x values up to L\n", "x=np.arange(0,L+.0000001,.0001)\n", "# python function that returns the psi for any selected case. \n", "# there is also a check to make sure the selection makes sense\n", "def phiFunc(x,type=1):\n", " L=x.max()\n", " if type==1: phi=np.sqrt(30)/L**2/np.sqrt(L)*x*(x-L)\n", " elif type==2: phi=x**6*np.sin(np.pi*x/L)/0.07931977085/L**6/np.sqrt(L)\n", " elif type==3: phi=np.sqrt(105)/L**3/np.sqrt(L)*x**2*(x-L)\n", " elif type==4: phi=np.sqrt(2/L)*np.sin(np.pi*x/L)\n", " elif type==5: phi=np.sqrt(495)/L**5/np.sqrt(L)*x*(x-L)**4\n", " elif type==6: phi=np.sqrt(2/L)*np.sin(2*np.pi*x/L)\n", " else: print('You did not enter a valid type (1,2,3,4,5,6)')\n", " return(phi)\n", "phi=phiFunc(x,type=2)" ] }, { "cell_type": "code", "execution_count": 10, "id": "434e6dae", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The mean position is: 1.6495899966964536\n" ] }, { "data": { "text/plain": [ "Text(0, 0.5, '$\\\\psi(x)$')" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#plotting the selected psi**2 (the probability density function for the position)\n", "plt.plot(x,phi**2)\n", "# computing the mean position using trapezoid integration np.trapz()\n", "xave=np.trapz(x*phi**2,x=x)\n", "# printing and plotting\n", "print('The mean position is:',xave)\n", "plt.plot([xave,xave],[0,np.max(phi**2)],'k--')\n", "plt.xlabel('x',fontsize=15)\n", "plt.ylabel(r'$\\psi(x)$',fontsize=15)" ] }, { "cell_type": "code", "execution_count": 11, "id": "093affc0", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The total probability is: 0.9999999999003251\n" ] } ], "source": [ "# computing the total probability to make sure it is properly normalized\n", "print('The total probability is:',np.trapz(phi**2,x=x))" ] }, { "cell_type": "code", "execution_count": 12, "id": "c1619bfb", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The probability of the particle in the left half is: 0.0014586291896360175\n", "The probability of the particle in the right half is: 0.9985394293430275\n", "The probability of the particle in the left the average is: 0.4475440893213001\n", "The probability of the particle in the central half is: 0.18977687591318337\n", "The probability of the particle in the outside half tails: 0.8102231240868166\n" ] } ], "source": [ "# computing various other probabilities as indicated in the handout\n", "jj=np.where(x<=L/2)\n", "print('The probability of the particle in the left half is:',np.trapz(phi[jj]**2,x=x[jj]))\n", "jj=np.where(x>L/2)\n", "print('The probability of the particle in the right half is:',np.trapz(phi[jj]**2,x=x[jj]))\n", "jj=np.where(x<=xave)\n", "print('The probability of the particle in the left the average is:',np.trapz(phi[jj]**2,x=x[jj]))\n", "jj=np.where((x>=L/4)&(x<3*L/4))\n", "inCenter=np.trapz(phi[jj]**2,x=x[jj])\n", "print('The probability of the particle in the central half is:',inCenter)\n", "print('The probability of the particle in the outside half tails:',1-inCenter)\n" ] }, { "cell_type": "code", "execution_count": 13, "id": "673c3e1e", "metadata": {}, "outputs": [], "source": [ "# now I try the first complex values wavefunction.\n", "# here I use (0+1j) as sqrt(-1)\n", "def psiFunc(x,k):\n", " L=x.max()\n", " psi=np.sqrt(2/L)*np.sin(np.pi*x/L)*np.exp((0+1j)*k*x)\n", " return(psi)\n", "psi=psiFunc(x,10)" ] }, { "cell_type": "code", "execution_count": 16, "id": "47d81a8f", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#plotting the real part, imaginary part, and probability density function\n", "plt.plot(x,psi.real,label='Real part')\n", "plt.plot(x,psi.imag,label='Imaginary part')\n", "plt.plot(x,psi.real**2+psi.imag**2,label='modulus square')\n", "plt.xlabel('x',fontsize=15)\n", "plt.ylabel(r'$\\psi(x)$',fontsize=15)\n", "plt.legend()" ] }, { "cell_type": "code", "execution_count": 17, "id": "809cbd02", "metadata": {}, "outputs": [], "source": [ "# same but for the second complex psi\n", "def psiB(x):\n", " L=x.max()\n", " psi=(1-np.exp(1-10*(0+1j)))*(np.exp((1+7*(0+1j))*(x-L)/L)-1)/2.1335722875015692/np.sqrt(L)\n", " return(psi)" ] }, { "cell_type": "code", "execution_count": 18, "id": "576def02", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "psi=psiB(x)\n", "plt.plot(x,psi.real,label='Real part')\n", "plt.plot(x,psi.imag,label='Imaginary part')\n", "plt.plot(x,psi.real**2+psi.imag**2,label='modulus square')\n", "plt.xlabel('x',fontsize=15)\n", "plt.ylabel(r'$\\psi(x)$',fontsize=15)\n", "plt.legend()" ] }, { "cell_type": "code", "execution_count": null, "id": "6d5a6f49", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.12" } }, "nbformat": 4, "nbformat_minor": 5 }