{
"metadata": {
"name": "",
"signature": "sha256:d58e11c98e937b7ff914fc9567035f99fc6ab344053f332f140829887d0ef6cc"
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"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"9: Quantum Mechanics"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 9.1, Page number 202"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"V = 100; #Accelerating potential for electron(volt)\n",
"\n",
"#Calculation\n",
"lamda = math.sqrt(150/V)*10**-10; #de-Broglie wavelength of electron(m)\n",
"\n",
"#Result\n",
"print \"The De-Broglie wavelength of electron is\",lamda, \"m\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The De-Broglie wavelength of electron is 1.22474487139e-10 m\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 9.2, Page number 203"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"e = 1.6*10**-19; #Energy equivalent of 1 eV(J/eV)\n",
"h = 6.626*10**-34; #Planck's constant(Js)\n",
"m = 9.11*10**-31; #Mass of the electron(kg)\n",
"Ek = 10; #Kinetic energy of electron(eV)\n",
"\n",
"#Calculation\n",
"p = math.sqrt(2*m*Ek*e); #Momentum of the electron(kg-m/s)\n",
"lamda = h/p ; #de-Broglie wavelength of electron from De-Broglie relation(m)\n",
"lamda = lamda*10**9; #de-Broglie wavelength of electron from De-Broglie relation(nm)\n",
"lamda = math.ceil(lamda*10**2)/10**2; #rounding off the value of lamda to 2 decimals\n",
"\n",
"#Result\n",
"print \"The de-Broglie wavelength of electron is\",lamda, \"nm\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The de-Broglie wavelength of electron is 0.39 nm\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 9.3, Page number 203. theoritical proof"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 9.4, Page number 203"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"h = 6.626*10**-34; #Planck's constant(Js)\n",
"m = 9.11*10**-31; #Mass of the electron(kg)\n",
"v = 1.1*10**6; #Speed of the electron(m/s)\n",
"pr = 0.1; #precision in percent\n",
"\n",
"#Calculation\n",
"p = m*v; #Momentum of the electron(kg-m/s)\n",
"dp = pr/100*p; #Uncertainty in momentum(kg-m/s)\n",
"h_bar = h/(2*math.pi); #Reduced Planck's constant(Js)\n",
"dx = h_bar/(2*dp); #Uncertainty in position(m)\n",
"\n",
"#Result\n",
"print \"The uncertainty in position of electron is\",dx, \"m\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The uncertainty in position of electron is 5.26175358211e-08 m\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 9.5, Page number 203"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"e = 1.6*10**-19; #Energy equivalent of 1 eV(J/eV)\n",
"h = 6.626*10**-34; #Planck's constant(Js)\n",
"dt = 10**-8; #Uncertainty in time(s)\n",
"\n",
"#Calculation\n",
"h_bar = h/(2*math.pi); #Reduced Planck's constant(Js)\n",
"dE = h_bar/(2*dt*e); #Uncertainty in energy of the excited state(m)\n",
"\n",
"#Result\n",
"print \"The uncertainty in energy of the excited state is\",dE, \"eV\"\n",
"\n",
"#answer given in the book is wrong"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The uncertainty in energy of the excited state is 3.2955020404e-08 eV\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 9.6, Page number 204"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"c = 3*10**8; #Speed of light(m/s)\n",
"dt = 10**-8; #Average lifetime(s)\n",
"lamda = 400; #Wavelength of spectral line(nm)\n",
"\n",
"#Calculation\n",
"lamda = lamda*10**-9; #Wavelength of spectral line(m)\n",
"#From Heisenberg uncertainty principle,\n",
"#dE = h_bar/(2*dt) and also dE = h*c/lambda^2*d_lambda, which give\n",
"#h_bar/(2*dt) = h*c/lambda^2*d_lambda, solving for d_lambda\n",
"d_lamda = (lamda**2)/(4*math.pi*c*dt); #Width of spectral line(m)\n",
"\n",
"#Result\n",
"print \"The width of spectral line is\",d_lamda, \"m\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The width of spectral line is 4.24413181578e-15 m\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 9.7, Page number 204. theoritical proof"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 9.8, Page number 204. theoritical proof"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 9.9, Page number 205. theoritical proof"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 9.10, Page number 205. theoritical proof"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 9.11, Page number 205. theoritical proof"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 9.12, Page number 206. theoritical proof"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 9.13, Page number 206. theoritical proof "
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 9.14, Page number 207"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"from scipy.integrate import quad\n",
"\n",
"#Variable declaration\n",
"a = 2*10**-10; # Width of 1D box(m)\n",
"x1=0; # Position of first extreme of the box(m)\n",
"x2=1*10**-10; # Position of second extreme of the box(m)\n",
"\n",
"#Calculation\n",
"def intg(x):\n",
" return ((2/a)*(math.sin(2*math.pi*x/a))**2)\n",
"S=quad(intg,x1,x2)[0]\n",
"\n",
"#Result\n",
"print \"The probability of finding the electron between x = 0 and x = 10**-10 is\",S"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The probability of finding the electron between x = 0 and x = 10**-10 is 0.5\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}