{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "#3(B):Principles of Quantum Mechanics" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##Example number 3.1, Page number 3.41" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Velocity = 1.38 *10**6 m/s\n", "Wavelength = 0.00286 Angstorm\n" ] } ], "source": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "KE=10 #Kinetic Energy of neutron in keV\n", "m=1.675*10**-27\n", "h=6.625*10**-34\n", "#Calculations\n", "KE=10**4*1.6*10**-19 #in joule\n", "v=((2*KE)/m)**(1/2) #derived from KE=1/2*m*v**2\n", "lamda=h/(m*v)\n", "#Results\n", "print\"Velocity =\",round(v/10**6,2),\"*10**6 m/s\"\n", "print\"Wavelength =\",round(lamda*10**10,5),\"Angstorm\"\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##Example number 3.2, Page number 3.41" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Momentum 2.4133\n", "de Brolie wavelength = 2.73 *10**-11 m\n" ] } ], "source": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "E=2*1000*1.6*10**-19 #in joules\n", "m=9.1*10**-31\n", "h=6.6*10*10**-34\n", "\n", "#Calculations\n", "p=math.sqrt(2*m*E)\n", "lamda= h/p\n", "\n", "#Result\n", "print\"Momentum\",round(p*10**23,4)\n", "print\"de Brolie wavelength =\",round(lamda*10**10,2),\"*10**-11 m\"\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##Example number 3.3, Page number 3.41" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "wavelength = 1.807 Angstorm\n" ] } ], "source": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "M=1.676*10**-27 #Mass of neutron\n", "m=0.025\n", "v=1.602*10**-19\n", "h=6.62*10**-34\n", "\n", "#Calculations\n", "mv=(2*m*v)**(1/2)\n", "lamda=h/(mv*M**(1/2))\n", "\n", "#Result\n", "print\"wavelength =\",round(lamda*10**10,3),\"Angstorm\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##Example number 3.4, Page number 3.42" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Wavelength = 0.1226 Angstorm\n" ] } ], "source": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "V=10000\n", "\n", "#Calculation\n", "lamda=12.26/math.sqrt(V)\n", "\n", "#Result\n", "print\"Wavelength =\",lamda,\"Angstorm\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##Example number 3.5, Page number 3.42" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The permitted electron energies = 38.0 *n**2 eV\n", "E1= 38.0 eV\n", "E2= 151.0 eV\n", "E3= 339.0 eV\n", "#Answer varies due to rounding of numbers\n" ] } ], "source": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "\n", "#Variable declaration\n", "e=1.6*10**-19; #charge of electron(coulomb)\n", "L=10**-10 #1Angstrom=10**-10 m\n", "n1=1;\n", "n2=2;\n", "n3=3;\n", "h=6.626*10**-34\n", "m=9.1*10**-31\n", "L=10**-10\n", "\n", "#Calculations\n", "E1=(h**2)/(8*m*L**2*e)\n", "E2=4*E1\n", "E3=9*E1\n", "#Result\n", "print\"The permitted electron energies =\",round(E1),\"*n**2 eV\"\n", "print\"E1=\",round(E1),\"eV\"\n", "print\"E2=\",round(E2),\"eV\"\n", "print\"E3=\",round(E3),\"eV\"\n", "print\"#Answer varies due to rounding of numbers\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##Example number 3.6, Page number 3.42" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "si**2 delta(x)= 0.2\n" ] } ], "source": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "i=1*10**-10; #interval\n", "L=10*10**-10; #width\n", "\n", "#Calculations\n", "si2=2*i/L;\n", "\n", "#Result\n", "print\"si**2 delta(x)=\",si2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##Example number 3.7, Page number 3.43" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " E1 = 1.81 *10**-37 Joule\n", "E2 = 3.62 *10**-37 Joule\n", "E2-E1 = 1.81 *10**-37 J\n" ] } ], "source": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "nx=1\n", "ny=1\n", "nz=1\n", "a=1\n", "h=6.63*10**-34\n", "m=9.1*10**-31\n", "\n", "#Calculations\n", "E1=h**2*(nx**2+ny**2+nz**2)/(8*m*a**2)\n", "E2=(h**2*6)/(8*m*a**2) #nx**2+ny**2+nz**2=6\n", "diff=E2-E1\n", "#Result\n", "print\"E1 =\",round(E1*10**37,2),\"*10**-37 Joule\"\n", "print\"E2 =\",round(E2*10**37,2),\"*10**-37 Joule\"\n", "print\"E2-E1 =\",round(diff*10**37,2),\"*10**-37 J\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##Example number 3.8, Page number 3.43" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "E1 = 3.28 *10**-13 J\n" ] } ], "source": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "m=1.67*10**-27\n", "a=10**-14\n", "h=1.054*10**-34\n", "\n", "#Calculations\n", "E1=(1*math.pi*h)**2/(2*m*a**2)\n", "\n", "#Result\n", "print\"E1 =\",round(E1*10**13,2),\"*10**-13 J\"\n" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "#Example number 3.9, Page number 3.44" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "a= 0.0158\n" ] } ], "source": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "from scipy.integrate import quad\n", "#Variable declarations\n", "k=1;\n", "\n", "#Calculations\n", "def zintg(x):\n", " return 2*k*math.exp(-2*k*x)\n", "a=quad(zintg,2/k,3/k)[0]\n", "\n", "#Result\n", "print \"a=\",round(a,4)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.9" } }, "nbformat": 4, "nbformat_minor": 0 }