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+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "collapsed": false
+ },
+ "source": [
+ "# Chapter 2:Band Theory of Solids"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "collapsed": true
+ },
+ "source": [
+ "## Example 2.1,Page No:2.2"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Lowest three permissable quantum energies are E1 = 6 eV\n",
+ " E2 = 24 eV\n",
+ " E3 = 54 eV\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "\n",
+ "#variable declaration\n",
+ "h = 6.63*10**-34; # plancks constant in J.s\n",
+ "m = 9.1*10**-31; # mass of electron in kg\n",
+ "a = 2.5*10**-10; # width of infinite square well\n",
+ "e = 1.6*10**-19; # charge of electron coulombs\n",
+ "n2 = 2; #number of permiissable quantum\n",
+ "n3 = 3; #number of permiissable quantum\n",
+ "\n",
+ "# Calculations\n",
+ "E1 = (h**2)/float(8*m*a**2*e); # first lowest permissable quantum energy in eV\n",
+ "E2 = n2**2 *E1; # second lowest permissable quantum energy in eV\n",
+ "E3 = n3**2 *E1; # second lowest permissable quantum energy in eV\n",
+ "\n",
+ "# Result\n",
+ "print'Lowest three permissable quantum energies are E1 = %d'%E1,'eV';\n",
+ "print' E2 = %d'%E2,'eV';\n",
+ "print' E3 = %d'%E3,'eV';"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 2.2,Page No:2.4"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Energy Difference = 113.21 eV\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "\n",
+ "#variable declaration\n",
+ "h = 6.63*10**-34; # plancks constant in J.s\n",
+ "m = 9.1*10**-31; # mass of electron in kg\n",
+ "a = 10**-10; # width of infinite square well in m\n",
+ "e = 1.6*10**-19; # charge of electron in coulombs\n",
+ "n1 = 1; #energy level constant\n",
+ "n2 = 2; #energy level constant\n",
+ "\n",
+ "# calculations\n",
+ "E1 = ((n1**2)*(h**2))/float(8*m*(a**2)*e); # ground state energy in eV\n",
+ "E2 = ((n2**2)*(h**2))/float(8*m*(a**2)*e); # first excited state in energy in eV\n",
+ "dE = E2-E1 # difference between first excited and ground state(E2 - E1)\n",
+ "\n",
+ "#Result\n",
+ "print'Energy Difference = %3.2f '%dE,'eV';\n",
+ "\n",
+ " \n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 2.3,Page No:2.5"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "First Three Energy levels are \n",
+ " E1 = 1.51 eV\n",
+ " E2 = 6 eV\n",
+ " E3 = 13.59 eV\n",
+ "\n",
+ " Above calculation shows that the energy of the bound electron cannot be continuous\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "\n",
+ "# Variable declaration\n",
+ "h = 6.63*10**-34; # plancks constant in J.s\n",
+ "m = 9.1*10**-31; # mass of electron in kg\n",
+ "a = 5*10**-10; # width of infinite potential well in m\n",
+ "e = 1.6*10**-19; # charge of electron in coulombs\n",
+ "n1 = 1; # energy level constant\n",
+ "n2 = 2; # energy level constant\n",
+ "n3 = 3; # energy level constant\n",
+ "\n",
+ "#Calculations\n",
+ "E1 = ((n1**2)*(h**2))/(8*m*(a**2)*e); # first energy level in eV\n",
+ "E2 = ((n2**2)*(h**2))/(8*m*(a**2)*e); # second energy level in eV\n",
+ "E3 = ((n3**2)*(h**2))/(8*m*(a**2)*e); # third energy level in eV\n",
+ "\n",
+ "# Result\n",
+ "print'First Three Energy levels are \\n E1 = %3.2f'%E1,'eV';\n",
+ "print' E2 = %d'%E2,'eV';\n",
+ "print' E3 = %3.2f'%E3,'eV';\n",
+ "print'\\n Above calculation shows that the energy of the bound electron cannot be continuous';\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 2.4,Page No:2.5"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Lowest energy bandwidth = 0.452 eV\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "\n",
+ "#variable declaration\n",
+ "h = 1.054*10**-34; #plancks constant in J.s\n",
+ "m = 9.1*10**-31; #mass of electron in kg\n",
+ "a = 5*10**-10; #width of infinite potential well in m\n",
+ "e = 1.6*10**-19; # charge of electron coulombs\n",
+ "\n",
+ "# Calculations\n",
+ "#cos(ka) = ((Psin(alpha*a))/(alpha*a)) + cos(alpha*a)\n",
+ "#to find the lowest allowed energy bandwidth,we have to find the difference in αa values, as ka changes from 0 to π\n",
+ "# for ka = 0 in above eq becomes\n",
+ "# 1 = 10*sin(αa))/(αa)) + cos(αa)\n",
+ "# This gives αa = 2.628 rad\n",
+ "# ka = π , αa = π\n",
+ "# sqrt((2*m*E2)/h**2)*a = π\n",
+ "\n",
+ "E2 = ((math.pi*math.pi)*h**2)/(2*m*a**2*e); #energy in eV\n",
+ "E1 = ((2.628**2)*h**2)/(2*m*a**2*e); #for αa = 2.628 rad energy in eV\n",
+ "dE = E2 - E1; #lowest energy bandwidth in eV\n",
+ "\n",
+ "# Result\n",
+ "print'Lowest energy bandwidth = %3.3f'%dE,'eV';\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 2.5,Page No:2.8"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Electron Momentum for first Brillouin zone appearance = 1.105e-24 eV\n",
+ "\n",
+ " Energy of free electron with this momentum = 4.2 eV\n",
+ "\n",
+ " Note: in Textbook Momentum value is wrongly printed as 1.1*10**-10\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "\n",
+ "# Variable declaration\n",
+ "a = 3*10**-10; # side of 2d square lattice in m\n",
+ "h = 6.63*10**-34; # plancks constant in J.s\n",
+ "e = 1.6*10**-19 # charge of electron in coulombs\n",
+ "m = 9.1*10**-31; # mass of electron in kg\n",
+ "\n",
+ "# calculations\n",
+ "#p = h*k # momentum of the electron\n",
+ "k = math.pi/float(a); # first Brillouin zone\n",
+ "p = (h/float(2*math.pi))*(math.pi/float(a)); # momentum of electron\n",
+ "E = (p**2)/float(2*m*e) # Energyin eV\n",
+ "\n",
+ "#Result\n",
+ "print'Electron Momentum for first Brillouin zone appearance = %g'%p,'eV';\n",
+ "print'\\n Energy of free electron with this momentum = %4.1f'%E,'eV';\n",
+ "print'\\n Note: in Textbook Momentum value is wrongly printed as 1.1*10**-10';"
+ ]
+ }
+ ],
+ "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": "2.7.6"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
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