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{
"metadata": {
"name": "",
"signature": "sha256:8884b20a8f08880d4a94501a9f3a466664f30ca1f04c541fe7d3a232f87a24bc"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"6: Quantum mechanics of simple systems"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 6.1, Page number 90"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from scipy.integrate import quad\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=2*10**-10; #length of square well(m)\n",
"\n",
"#Calculation\n",
"def intg(x):\n",
" return (2/a)*(math.sin(math.pi*x/a))**2\n",
"\n",
"S=quad(intg,0,0.25*10**-10)[0] #probability of finding the electron\n",
"\n",
"#Result\n",
"print \"probability of finding the electron is\",round(S,4)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"probability of finding the electron is 0.0125\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 6.2, Page number 96"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#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",
"new0=6.43*10**13; #frequency(Hz)\n",
"e=1.6*10**-19; #conversion factor from J to eV\n",
"mew=1.1385*10**-26; #reduced mass(kg)\n",
"\n",
"#Calculation\n",
"E0=h*new0/2; #zero point energy(J)\n",
"E0=E0/e; #zero point energy(eV)\n",
"k=4*math.pi**2*new0**2*mew; #force constane(N/m)\n",
"\n",
"#Result\n",
"print \"zero point energy is\",round(E0,3),\"eV\"\n",
"print \"force constane is\",round(k),\"N/m\"\n",
"print \"answer varies due to rounding off errors\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"zero point energy is 0.133 eV\n",
"force constane is 1858.0 N/m\n",
"answer varies due to rounding off errors\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 6.6, Page number 104"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"m1=19.9217*10**-27; #mass of carbon atom(kg)\n",
"m2=26.5614*10**-27; #mass of oxygen atom(kg)\n",
"r=1.131*10**-10; #separation(m)\n",
"hbar=1.054*10**-34;\n",
"e=1.6*10**-19; #conversion factor from J to eV\n",
"\n",
"#Calculation\n",
"mew=(m1*m2)/(m1+m2); #reduced mass(kg)\n",
"I=mew*r**2; \n",
"deltaE=hbar**2/I; #energy difference(J)\n",
"deltaE=deltaE/e; #energy difference(eV)\n",
"\n",
"#Result\n",
"print \"energy difference is\",round(deltaE*10**4,2),\"*10**-4 eV\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"energy difference is 4.77 *10**-4 eV\n"
]
}
],
"prompt_number": 21
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 6.7, Page number 105"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"m1=1;\n",
"m2=0;\n",
"m3=-1; #m-components\n",
"l=1;\n",
"\n",
"#Calculation\n",
"L=math.sqrt(l*(l+1)); #length of vector\n",
"theta1=math.acos(m1/L); #orientation for m=1(radian)\n",
"theta1=theta1*180/math.pi; #orientation for m=1(degrees)\n",
"theta2=math.acos(m2/L); #orientation for m=0(radian)\n",
"theta2=theta2*180/math.pi; #orientation for m=0(degrees)\n",
"theta3=math.acos(m3/L); #orientation for m=-1(radian)\n",
"theta3=theta3*180/math.pi; #orientation for m=-1(degrees)\n",
"\n",
"#Result\n",
"print \"orientation for m=1 is\",theta1,\"degrees\"\n",
"print \"orientation for m=0 is\",theta2,\"degrees\"\n",
"print \"orientation for m=-1 is\",theta3,\"degrees\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"orientation for m=1 is 45.0 degrees\n",
"orientation for m=0 is 90.0 degrees\n",
"orientation for m=-1 is 135.0 degrees\n"
]
}
],
"prompt_number": 22
}
],
"metadata": {}
}
]
}
|
