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-{
- "cells": [
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "# 6: Principles of Quantum Mechanics"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Example number 1, Page number 6.22"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 2,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "deBroglie wavelength is 0.66 angstrom\n",
- "spacing between planes is 0.35 angstrom\n"
- ]
- }
- ],
- "source": [
- "#importing modules\n",
- "import math\n",
- "from __future__ import division\n",
- "\n",
- "#Variable declaration\n",
- "V=344; #voltage(V)\n",
- "theta=40; #angle(degrees)\n",
- "n=1; \n",
- "\n",
- "#Calculation\n",
- "lamda=12.26/math.sqrt(V); #deBroglie wavelength(angstrom)\n",
- "theta=((180-theta)/2)*math.pi/180; #angle(radian)\n",
- "d=n*lamda/(2*math.sin(theta)); #spacing between planes(angstrom)\n",
- "\n",
- "#Result\n",
- "print \"deBroglie wavelength is\",round(lamda,2),\"angstrom\"\n",
- "print \"spacing between planes is\",round(d,2),\"angstrom\""
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Example number 2, Page number 6.22"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 6,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "deBroglie wavelength is 0.00286 angstrom\n"
- ]
- }
- ],
- "source": [
- "#importing modules\n",
- "import math\n",
- "from __future__ import division\n",
- "\n",
- "#Variable declaration\n",
- "e=1.6*10**-19; #charge(coulomb)\n",
- "m=1.675*10**-27; #mass(kg)\n",
- "E=10*10**3*e; #kinetic energy(J)\n",
- "h=6.625*10**-34; #planks constant(Js)\n",
- "\n",
- "#Calculation\n",
- "v=math.sqrt(2*E/m); #velocity(m/sec)\n",
- "lamda=h*10**10/(m*v); #deBroglie wavelength(angstrom)\n",
- "\n",
- "#Result\n",
- "print \"deBroglie wavelength is\",round(lamda,5),\"angstrom\""
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Example number 3, Page number 6.22"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 8,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "energy difference is 1.81 *10**-37 J\n"
- ]
- }
- ],
- "source": [
- "#importing modules\n",
- "import math\n",
- "from __future__ import division\n",
- "\n",
- "#Variable declaration\n",
- "m=9.1*10**-31; #mass(kg)\n",
- "h=6.63*10**-34; #planks constant(Js)\n",
- "a=1; #length(m)\n",
- "nx1=1;\n",
- "ny1=1;\n",
- "nz1=1;\n",
- "nx2=1;\n",
- "ny2=1;\n",
- "nz2=2;\n",
- "\n",
- "#Calculation\n",
- "E1=h**2*(nx1**2+ny1**2+nz1**2)/(8*m*a**2); #energy of 1st quantum state(J)\n",
- "E2=h**2*(nx2**2+ny2**2+nz2**2)/(8*m*a**2); #energy of 2nd quantum state(J)\n",
- "E=E2-E1; #energy difference(J)\n",
- "\n",
- "#Result\n",
- "print \"energy difference is\",round(E*10**37,2),\"*10**-37 J\""
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Example number 4, Page number 6.23"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 12,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "uncertainity in position of electron is 0.002 m\n",
- "uncertainity in position of bullet is 0.4 *10**-31 m\n"
- ]
- }
- ],
- "source": [
- "#importing modules\n",
- "import math\n",
- "from __future__ import division\n",
- "\n",
- "#Variable declaration\n",
- "m1=9.1*10**-31; #mass(kg)\n",
- "m2=0.05; #mass(kg)\n",
- "v=300; #velocity(m/sec)\n",
- "p=0.01/100; #probability\n",
- "h=6.6*10**-34; #planks constant(Js)\n",
- "\n",
- "#Calculation\n",
- "p1=m1*v; #momentum of electron(kg m/s)\n",
- "deltap1=p*p1; \n",
- "deltax1=h/(deltap1*4*math.pi); #uncertainity in position of electron(m)\n",
- "p2=m2*v; #momentum of bullet(kg m/s)\n",
- "deltap2=p*p2; \n",
- "deltax2=h/(deltap2*4*math.pi); #uncertainity in position of bullet(m)\n",
- "\n",
- "#Result\n",
- "print \"uncertainity in position of electron is\",round(deltax1,3),\"m\"\n",
- "print \"uncertainity in position of bullet is\",round(deltax2*10**31,1),\"*10**-31 m\""
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Example number 5, Page number 6.24"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 13,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "probability of finding the particle is 0.2\n"
- ]
- }
- ],
- "source": [
- "#importing modules\n",
- "import math\n",
- "from __future__ import division\n",
- "\n",
- "#Variable declaration\n",
- "deltax=10**-10; #uncertainity in position(m)\n",
- "L=10*10**-10; #width(m)\n",
- "\n",
- "#Calculation\n",
- "p=2*deltax/L; #probability of finding the particle\n",
- "\n",
- "#Result\n",
- "print \"probability of finding the particle is\",p"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Example number 6, Page number 6.24"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 15,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "deBroglie wavelength is 2.73 *10**-11 m\n"
- ]
- }
- ],
- "source": [
- "#importing modules\n",
- "import math\n",
- "from __future__ import division\n",
- "\n",
- "#Variable declaration\n",
- "e=1.6*10**-19; #charge(coulomb)\n",
- "m=9.1*10**-31; #mass(kg)\n",
- "E=2*10**3*e; #kinetic energy(J)\n",
- "h=6.6*10**-34; #planks constant(Js)\n",
- "\n",
- "#Calculation\n",
- "p=math.sqrt(2*E*m); #momentum(kg m/s)\n",
- "lamda=h/p; #deBroglie wavelength(m)\n",
- "\n",
- "#Result\n",
- "print \"deBroglie wavelength is\",round(lamda*10**11,2),\"*10**-11 m\""
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Example number 7, Page number 6.24"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 21,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "deBroglie wavelength is 1.807 angstrom\n"
- ]
- }
- ],
- "source": [
- "#importing modules\n",
- "import math\n",
- "from __future__ import division\n",
- "\n",
- "#Variable declaration\n",
- "e=1.602*10**-19; #charge(coulomb)\n",
- "m=1.676*10**-27; #mass(kg)\n",
- "h=6.62*10**-34; #planks constant(Js)\n",
- "E=0.025*e; #kinetic energy(J)\n",
- "\n",
- "#Calculation\n",
- "mv=math.sqrt(2*E*m); #velocity(m/s)\n",
- "lamda=h*10**10/mv; #deBroglie wavelength(angstrom)\n",
- "\n",
- "#Result\n",
- "print \"deBroglie wavelength is\",round(lamda,3),\"angstrom\""
- ]
- }
- ],
- "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": "2.7.11"
- }
- },
- "nbformat": 4,
- "nbformat_minor": 0
-}
generated by cgit (git 2.34.1) at 2024-12-19 14:48:24 +0000