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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
+}
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