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authorTrupti Kini2016-09-26 23:32:22 +0600
committerTrupti Kini2016-09-26 23:32:22 +0600
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Added(A)/Deleted(D) following books
M Basic_Electronics_Electronics_Engineering_by_J_B_Gupta/README.txt M Modern_Digital_And_Analog_Communication_System_by_B._P._Lathi/Chapter10_1.ipynb M Modern_Digital_And_Analog_Communication_System_by_B._P._Lathi/Chapter11_1.ipynb M Modern_Digital_And_Analog_Communication_System_by_B._P._Lathi/Chapter12_1.ipynb M Modern_Digital_And_Analog_Communication_System_by_B._P._Lathi/Chapter13_1.ipynb M Modern_Digital_And_Analog_Communication_System_by_B._P._Lathi/Chapter14_1.ipynb M Modern_Digital_And_Analog_Communication_System_by_B._P._Lathi/Chapter15_1.ipynb M Modern_Digital_And_Analog_Communication_System_by_B._P._Lathi/Chapter16_1.ipynb M Modern_Digital_And_Analog_Communication_System_by_B._P._Lathi/Chapter2_1.ipynb M Modern_Digital_And_Analog_Communication_System_by_B._P._Lathi/Chapter3_1.ipynb M Modern_Digital_And_Analog_Communication_System_by_B._P._Lathi/Chapter4_1.ipynb M Modern_Digital_And_Analog_Communication_System_by_B._P._Lathi/Chapter5_1.ipynb M Modern_Digital_And_Analog_Communication_System_by_B._P._Lathi/Chapter6_1.ipynb M Modern_Digital_And_Analog_Communication_System_by_B._P._Lathi/Chapter7_1.ipynb M Modern_Digital_And_Analog_Communication_System_by_B._P._Lathi/Chapter8_1.ipynb M Modern_Digital_And_Analog_Communication_System_by_B._P._Lathi/screenshots/2correlationCoeff_1.png M Modern_Digital_And_Analog_Communication_System_by_B._P._Lathi/screenshots/2expansionofSignal_1.png M Modern_Digital_And_Analog_Communication_System_by_B._P._Lathi/screenshots/2timeInvertedsignal_1.png M Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter10_1.ipynb M Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter11_1.ipynb M Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter15_1.ipynb M Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter1_1.ipynb M Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter2_1.ipynb M Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter3_1.ipynb M Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter5_1.ipynb M Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter6_1.ipynb M Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter7_1.ipynb M Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter8_1.ipynb M Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter9_1.ipynb M Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/screenshots/ctftch1.png M Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/screenshots/fourierTransch1.png M Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/screenshots/modulatedWaveChap3_1.png M Principles_of_Electronics_____by_V.K._Mehta_and_Rohit_Mehta/README.txt M Solid_State_Electronic_Devices_by_D.K_Bhattacharya_,_Rajnish_Sharma/Chapter10_1.ipynb M Solid_State_Electronic_Devices_by_D.K_Bhattacharya_,_Rajnish_Sharma/Chapter11_1.ipynb M Solid_State_Electronic_Devices_by_D.K_Bhattacharya_,_Rajnish_Sharma/Chapter12_1.ipynb M Solid_State_Electronic_Devices_by_D.K_Bhattacharya_,_Rajnish_Sharma/Chapter1_1.ipynb M Solid_State_Electronic_Devices_by_D.K_Bhattacharya_,_Rajnish_Sharma/Chapter2_1.ipynb M Solid_State_Electronic_Devices_by_D.K_Bhattacharya_,_Rajnish_Sharma/Chapter3_1.ipynb M Solid_State_Electronic_Devices_by_D.K_Bhattacharya_,_Rajnish_Sharma/Chapter4_1.ipynb M Solid_State_Electronic_Devices_by_D.K_Bhattacharya_,_Rajnish_Sharma/Chapter5_1.ipynb M Solid_State_Electronic_Devices_by_D.K_Bhattacharya_,_Rajnish_Sharma/Chapter6_1.ipynb M Solid_State_Electronic_Devices_by_D.K_Bhattacharya_,_Rajnish_Sharma/Chapter7_1.ipynb M Solid_State_Electronic_Devices_by_D.K_Bhattacharya_,_Rajnish_Sharma/Chapter8_1.ipynb M Solid_State_Electronic_Devices_by_D.K_Bhattacharya_,_Rajnish_Sharma/Chapter9_1.ipynb M Solid_State_Electronic_Devices_by_D.K_Bhattacharya_,_Rajnish_Sharma/chapter13_1.ipynb M Solid_State_Electronic_Devices_by_D.K_Bhattacharya_,_Rajnish_Sharma/chapter14_1.ipynb M Solid_State_Electronic_Devices_by_D.K_Bhattacharya_,_Rajnish_Sharma/screenshots/Chapter10.png M Solid_State_Electronic_Devices_by_D.K_Bhattacharya_,_Rajnish_Sharma/screenshots/Chapter1_1.png M Solid_State_Electronic_Devices_by_D.K_Bhattacharya_,_Rajnish_Sharma/screenshots/Chapter5.png M Solutions_to_Problems_in_Applied_Mechanics_by_A._N._Gobby/README.txt M Theory_of_Alternating_Current_Machinery_by_A._S._Langsdorf/README.txt M Thermodynamics_by_Gaggioli_and_Obert/Ch18.ipynb M Thermodynamics_by_Gaggioli_and_Obert/Ch8.ipynb M Thermodynamics_by_Gaggioli_and_Obert/ch1.ipynb M Thermodynamics_by_Gaggioli_and_Obert/ch10.ipynb M Thermodynamics_by_Gaggioli_and_Obert/ch11.ipynb M Thermodynamics_by_Gaggioli_and_Obert/ch12.ipynb M Thermodynamics_by_Gaggioli_and_Obert/ch13.ipynb M Thermodynamics_by_Gaggioli_and_Obert/ch14.ipynb M Thermodynamics_by_Gaggioli_and_Obert/ch15.ipynb M Thermodynamics_by_Gaggioli_and_Obert/ch16.ipynb M Thermodynamics_by_Gaggioli_and_Obert/ch17.ipynb M Thermodynamics_by_Gaggioli_and_Obert/ch2.ipynb M Thermodynamics_by_Gaggioli_and_Obert/ch3.ipynb M Thermodynamics_by_Gaggioli_and_Obert/ch5.ipynb M Thermodynamics_by_Gaggioli_and_Obert/ch7.ipynb M Thermodynamics_by_Gaggioli_and_Obert/ch9.ipynb M Thermodynamics_by_Gaggioli_and_Obert/screenshots/changeInMoisture14.png M Thermodynamics_by_Gaggioli_and_Obert/screenshots/degreeOfSaturation14.png M Thermodynamics_by_Gaggioli_and_Obert/screenshots/humidityratio14.png A Unified_Physics_by_S.L._Gupta,_Sanjeev_Gupta/Chapter1.ipynb A Unified_Physics_by_S.L._Gupta,_Sanjeev_Gupta/Chapter10.ipynb A Unified_Physics_by_S.L._Gupta,_Sanjeev_Gupta/Chapter11.ipynb A Unified_Physics_by_S.L._Gupta,_Sanjeev_Gupta/Chapter12.ipynb A Unified_Physics_by_S.L._Gupta,_Sanjeev_Gupta/Chapter14.ipynb A Unified_Physics_by_S.L._Gupta,_Sanjeev_Gupta/Chapter15.ipynb A Unified_Physics_by_S.L._Gupta,_Sanjeev_Gupta/Chapter16.ipynb A Unified_Physics_by_S.L._Gupta,_Sanjeev_Gupta/Chapter2.ipynb A Unified_Physics_by_S.L._Gupta,_Sanjeev_Gupta/Chapter3.ipynb A Unified_Physics_by_S.L._Gupta,_Sanjeev_Gupta/Chapter4.ipynb A Unified_Physics_by_S.L._Gupta,_Sanjeev_Gupta/Chapter5.ipynb A Unified_Physics_by_S.L._Gupta,_Sanjeev_Gupta/Chapter6.ipynb A Unified_Physics_by_S.L._Gupta,_Sanjeev_Gupta/Chapter7.ipynb A Unified_Physics_by_S.L._Gupta,_Sanjeev_Gupta/Chapter9.ipynb A Unified_Physics_by_S.L._Gupta,_Sanjeev_Gupta/screenshots/1.png A Unified_Physics_by_S.L._Gupta,_Sanjeev_Gupta/screenshots/2.png A Unified_Physics_by_S.L._Gupta,_Sanjeev_Gupta/screenshots/3.png M f_by_134/1_An_overview_of_C++.ipynb A f_by_134/1_An_overview_of_C++_1.ipynb A f_by_134/screenshots/anshul.png A f_by_134/screenshots/anshul_1.png A f_by_134/screenshots/anshul_2.png M f_by_134/screenshots/chapter14_eg3.png M f_by_134/screenshots/chapter14_eg6.png M f_by_134/screenshots/chapter14_eg6_1.png M f_by_df/ashvani.ipynb M f_by_df/chapter03_16.ipynb M f_by_df/chapter03_16_1.ipynb M f_by_df/screenshots/1.png M f_by_df/screenshots/2.png M f_by_df/screenshots/3.png M f_by_df/screenshots/chapter14_eg10.png M f_by_df/screenshots/chapter14_eg3.png M f_by_df/screenshots/chapter14_eg6.png M f_by_df/screenshots/image.png M f_by_df/screenshots/image_1.png M f_by_df/screenshots/image_2.png M sample_notebooks/AditiMalik/Chapter6.ipynb M sample_notebooks/IshitaGupta/Chapter12.ipynb M sample_notebooks/MeenaChandrupatla/Chapter2_Gases_2.ipynb M sample_notebooks/RONAKBANSAL/chapter_1.ipynb M sample_notebooks/SufiyanSiddique/Chapter2.ipynb M sample_notebooks/asmitaasmita/1_An_overview_of_C++.ipynb M sample_notebooks/asmitaasmita/1_An_overview_of_C++_1.ipynb A sample_notebooks/asmitaasmita/1_An_overview_of_C++_2.ipynb M sample_notebooks/chayas/DimensionsSystemUnits.ipynb
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+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# 6: Schroedinger Wave Equation"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 1, Page number 211"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "least energy is 37.65 eV\n",
+ "answer given in the book is wrong\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration \n",
+ "h=6.63*10**-34; #plancks constant(J sec)\n",
+ "m=9.11*10**-31; #mass(kg)\n",
+ "a=10**-10; #width of box(m)\n",
+ "e=1.602*10**-19; #charge(coulomb)\n",
+ "\n",
+ "#Calculations\n",
+ "E1=(h**2)/(8*m*e*a**2); #least energy(eV)\n",
+ "\n",
+ "#Result\n",
+ "print \"least energy is\",round(E1,2),\"eV\"\n",
+ "print \"answer given in the book is wrong\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 2, Page number 211"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "probability of finding the particle is 0.4\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration \n",
+ "delta_x=5*10**-10; #interval(m)\n",
+ "a=25*10**-10; #width(m)\n",
+ "\n",
+ "#Calculations\n",
+ "P=2*delta_x/a; #probability of finding the particle\n",
+ "\n",
+ "#Result\n",
+ "print \"probability of finding the particle is\",P"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 3, Page number 212"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "probability of finding the particle is 19.84 %\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "from scipy.integrate import quad\n",
+ "\n",
+ "#Variable declaration \n",
+ "a=1; #assume\n",
+ "\n",
+ "#Calculations\n",
+ "def zintg(x):\n",
+ " return (2/a)*(1/2)*(1-math.cos(2*math.pi*x/a))\n",
+ "\n",
+ "P1=quad(zintg,0.45,0.55)[0]\n",
+ "\n",
+ "#Result\n",
+ "print \"probability of finding the particle is\",round(P1*100,2),\"%\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 4, Page number 213"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " least energy is 6 eV\n",
+ "energy in 2nd excited state is 24 eV\n",
+ "energy in 3rd excited state is 54 eV\n",
+ "difference of energy between 2nd and 1st excited states is 18 eV\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration \n",
+ "h=6.63*10**-34; #planks constant(Js)\n",
+ "m=9.1*10**-31; #mass(kg)\n",
+ "a=2.5*10**-10; #width(m)\n",
+ "e=1.6*10**-19; #charge(coulomb)\n",
+ "n1=1; \n",
+ "n2=2;\n",
+ "n3=3; #energy states\n",
+ "\n",
+ "#Calculations\n",
+ "E1=n1**2*(h**2)/(8*m*e*a**2); #least energy(eV)\n",
+ "E2=n2**2*E1; #energy in 2nd excited state(eV)\n",
+ "E3=n3**2*E1; #energy in 3rd excited state(eV)\n",
+ "delta_E=E2-E1; #difference of energy between 2nd and 1st excited states(eV)\n",
+ "\n",
+ "#Result\n",
+ "print \"least energy is\",int(E1),\"eV\"\n",
+ "print \"energy in 2nd excited state is\",int(E2),\"eV\"\n",
+ "print \"energy in 3rd excited state is\",int(E3),\"eV\"\n",
+ "print \"difference of energy between 2nd and 1st excited states is\",int(delta_E),\"eV\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 5, Page number 213"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 23,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "de-Broglie wavelength of first three energy states are 20 angstrom 10 angstrom 6.67 angstrom\n",
+ "energies of first three energy states are 0.38 eV 1.5095 eV 3.396 eV\n",
+ "answer in the book varies due to rounding off errors\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration \n",
+ "h=6.63*10**-34; #planks constant(Js)\n",
+ "m=9.1*10**-31; #mass(kg)\n",
+ "a=10; #width(angstrom)\n",
+ "e=1.6*10**-19; #charge(coulomb)\n",
+ "n1=1; \n",
+ "n2=2;\n",
+ "n3=3; #energy states\n",
+ "\n",
+ "#Calculations\n",
+ "lamda1=2*a/n1; #de-Broglie wavelength of first energy state(angstrom)\n",
+ "lamda2=2*a/n2; #de-Broglie wavelength of second energy state(angstrom)\n",
+ "lamda3=2*a/n3; #de-Broglie wavelength of third energy state(angstrom)\n",
+ "E1=n1**2*(h**2)/(8*m*e*(a*10**-10)**2); #energy in 1st excited state(eV)\n",
+ "E2=n2**2*E1; #energy in 2nd excited state(eV)\n",
+ "E3=n3**2*E1; #energy in 3rd excited state(eV)\n",
+ "\n",
+ "#Result\n",
+ "print \"de-Broglie wavelength of first three energy states are\",int(lamda1),\"angstrom\",int(lamda2),\"angstrom\",round(lamda3,2),\"angstrom\"\n",
+ "print \"energies of first three energy states are\",round(E1,2),\"eV\",round(E2,4),\"eV\",round(E3,3),\"eV\"\n",
+ "print \"answer in the book varies due to rounding off errors\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 6, Page number 214"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 33,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "energy in 1st excited state is 14.7 *10**-19 J\n",
+ "mass is 9.3 *10**-31 kg\n",
+ "quantum state is 10.4\n",
+ "as n is not an integer, En is not permitted value of energy\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration \n",
+ "h=6.63*10**-34; #planks constant(Js)\n",
+ "a=0.2*10**-9; #width(m)\n",
+ "e=1.602*10**-19; #charge(coulomb)\n",
+ "n5=5; #energy state\n",
+ "E5=230*e; #energy 0f 5th state(J)\n",
+ "En=10**3*e; #energy(eV)\n",
+ "\n",
+ "#Calculations\n",
+ "E1=E5/n5**2; #energy in 1st excited state(eV)\n",
+ "m=h**2/(8*E1*a**2); #mass(kg)\n",
+ "n=math.sqrt(En/E1); #quantum state\n",
+ "\n",
+ "#Result\n",
+ "print \"energy in 1st excited state is\",round(E1*10**19,1),\"*10**-19 J\"\n",
+ "print \"mass is\",round(m*10**31,1),\"*10**-31 kg\"\n",
+ "print \"quantum state is\",round(n,1)\n",
+ "print \"as n is not an integer, En is not permitted value of energy\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 7, Page number 225"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 48,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "reflection coefficient in 1st case is 0.05\n",
+ "answer given in the book is wrong\n",
+ "transmission coefficient in 1st case is 0.95\n",
+ "for E=0.025, E<V. so transmission coefficient is 0 and reflection coefficient is 1\n",
+ "reflection coefficient in 3rd case is 1\n",
+ "transmission coefficient in 3rd case is 0\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",
+ "E1=0.04*e; #energy(J)\n",
+ "V=0.03*e; #energy barrier(J) \n",
+ "E2=0.025*e; #energy(J)\n",
+ "E3=0.03*e; #energy(J)\n",
+ "m=1; #assume \n",
+ "k1=1; #assume\n",
+ "\n",
+ "#Calculations\n",
+ "x=math.sqrt(E1-V);\n",
+ "y=math.sqrt(E1+V);\n",
+ "R1=((math.sqrt(E1)-x)/(math.sqrt(E1)+y))**2; #reflection coefficient\n",
+ "T1=1-R; #transmission coefficient\n",
+ "k2=math.sqrt(2*m*(E3-V)); \n",
+ "R2=((k1-k2)/(k1+k2))**2; #reflection coefficient\n",
+ "T2=4*k1*k2/(k1+k2)**2; #transmission coefficient \n",
+ "\n",
+ "#Result\n",
+ "print \"reflection coefficient in 1st case is\",round(R1,2)\n",
+ "print \"answer given in the book is wrong\"\n",
+ "print \"transmission coefficient in 1st case is\",round(T1,2)\n",
+ "print \"for E=0.025, E<V. so transmission coefficient is 0 and reflection coefficient is 1\"\n",
+ "print \"reflection coefficient in 3rd case is\",int(R2)\n",
+ "print \"transmission coefficient in 3rd case is\",int(T2)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 8, Page number 226"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 54,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "value of E/V is 1.03\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration \n",
+ "T=0.5; #transmission coefficient \n",
+ "a=1;\n",
+ "b=6;\n",
+ "c=1;\n",
+ "\n",
+ "#Calculations\n",
+ "k1byk2=(b+math.sqrt((b**2)-(4*a*c)))/(2*a); \n",
+ "x=k1byk2**2;\n",
+ "EbyV=x/(x-1); #value of E/V\n",
+ "\n",
+ "#Result\n",
+ "print \"value of E/V is\",round(EbyV,2)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 9, Page number 226"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 40,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "transmission probabilities in 1st case are 4.5 *10**-5 and 1.4 *10**-4\n",
+ "transmission probabilities in 2nd case are 2.1 *10**-9 and 1.25 *10**-9\n",
+ "answer for transmission probability in 2nd case given in the book is wrong\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",
+ "a1=5*10**-10; #width(m)\n",
+ "a2=10*10**-10; #width(m)\n",
+ "e=1.6*10**-19; #charge(coulomb)\n",
+ "V0=5; #energy barrier(eV)\n",
+ "E1=1; #energy of electron(eV)\n",
+ "E2=2;\n",
+ "chi=1.054*10**-34; #plancks constant(Js)\n",
+ "\n",
+ "#Calculations\n",
+ "beta1=math.sqrt(2*m*(V0-E1)*e/chi**2); #value of beta(m-1)\n",
+ "x1=int(-2*a1*beta1);\n",
+ "beta2=math.sqrt(2*m*(V0-E2)*e/chi**2); #value of beta(m-1)\n",
+ "x2=round(-2*a1*beta2,1);\n",
+ "T1=math.exp(x1); #transmission probability in 1st case\n",
+ "T2=math.exp(x2); #transmission probability in 1st case\n",
+ "x3=int(-2*a2*beta1);\n",
+ "x4=round(-2*a2*beta1,1);\n",
+ "T1dash=math.exp(x3); #transmission probability in 2nd case\n",
+ "T2dash=math.exp(x4); #transmission probability in 1st case\n",
+ "\n",
+ "#Result\n",
+ "print \"transmission probabilities in 1st case are\",round(T1*10**5,1),\"*10**-5 and\",round(T2*10**4,1),\"*10**-4\"\n",
+ "print \"transmission probabilities in 2nd case are\",round(T1dash*10**9,1),\"*10**-9 and\",round(T2dash*10**9,2),\"*10**-9\"\n",
+ "print \"answer for transmission probability in 2nd case given in the book is wrong\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 10, Page number 227"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 59,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "transmission coefficient is 4 math.exp ( -1.625 )\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",
+ "a=10**-10; #width(m)\n",
+ "e=1.6*10**-19; #charge(coulomb)\n",
+ "V0=5; #energy barrier(eV)\n",
+ "E=2.5; #energy of electron(eV)\n",
+ "chi=1.05*10**-34; #plancks constant(Js)\n",
+ "\n",
+ "#Calculations\n",
+ "x=16*E*(V0-E)/V0**2;\n",
+ "y=-2*a*math.sqrt(2*m*(V0-E)*e/chi**2);\n",
+ "#T=x*math.exp(y); #transmission coefficient\n",
+ "\n",
+ "#Result\n",
+ "print \"transmission coefficient is\",int(x),\"math.exp (\",round(y,3),\")\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 11, Page number 227"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 76,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "average lifetime of nucleus is 3.7 *10**17 years\n",
+ "answer given in the book is wrong\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration \n",
+ "P=10**21; #probability(T per sec)\n",
+ "m=4*1.6*10**-27; #mass(kg)\n",
+ "a=2*10**-14; #width(m)\n",
+ "e=1.67*10**-19; #charge(coulomb)\n",
+ "V0=30; #energy barrier(eV)\n",
+ "E=4.2; #energy of electron(eV)\n",
+ "chi=1.05*10**-34; #plancks constant(Js)\n",
+ "\n",
+ "#Calculations\n",
+ "x=P*16*E*(V0-E)/V0**2;\n",
+ "y=-2*a*math.sqrt(2*m*(V0-E)*10**6*e/chi**2);\n",
+ "T=x*math.exp(y); #transmission coefficient\n",
+ "tow=1/T; #average lifetime of nucleus(years) \n",
+ "\n",
+ "#Result\n",
+ "print \"average lifetime of nucleus is\",round(tow/10**17,1),\"*10**17 years\"\n",
+ "print \"answer given in the book is wrong\""
+ ]
+ }
+ ],
+ "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,
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