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{
"metadata": {
"name": "",
"signature": "sha256:846e8e3b3770f7cb30a2e91a53718bf5de841338951843c54481c2acfda5e63d"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 6: Quantum Mechanics in One Dimension"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.4, page no. 197"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" \n",
"\n",
"import math\n",
"\n",
"#Variable declaration\n",
"\n",
"me = 9.11 * 10 ** -31 #mass of electron (kg)\n",
"h = 1.055 * 10**-34 #h/2*pi (J.s)\n",
"dx0 = 1.0 * 10**-10 #initial location of electron(m)\n",
"m = 1.0 * 10**-3 #mass of marble (kg)\n",
"dx0m = 10**-4 #initial location of marble (m)\n",
"\n",
"#Calculation\n",
"\n",
"te = math.sqrt(99)* (2* me / h) * dx0**2\n",
"tm = math.sqrt(99)* (2* m / h) * dx0m**2\n",
"\n",
"#result\n",
"\n",
"print \"The time elapsed for electron is\",round(te/10**-15,1),\"X 10^-15 s and that of marble is \",round(tm/10**24,1),\"X 10^24 s.\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The time elapsed for electron is 1.7 X 10^-15 s and that of marble is 1.9 X 10^24 s.\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.5, page no. 202"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import math\n",
"\n",
"#Variable declaration\n",
"\n",
"m = 1.0 * 10 **-6 #mass (kg)\n",
"h = 6.626 * 10 **-34 #Planck's constant(J.s)\n",
"n = 1.0\n",
"L = 1.0 * 10**-2 #separation(m)\n",
"\n",
"#Calculation\n",
"\n",
"E1 = n**2 * h**2 /(8*m*L**2)\n",
"v1 = math.sqrt(2*E1/m)\n",
"\n",
"#result\n",
"\n",
"print \"(a) The minimum speed of the particle is\",round(v1/10**-26,2),\"X 10^-26 m/s.\"\n",
"\n",
"\n",
"#Variable declaration\n",
"\n",
"v = 3.00 * 10**-2 #speed of the particle (m/s)\n",
"\n",
"#Calculation\n",
"\n",
"E = m* v**2 /2\n",
"n = math.sqrt(8*m*L**2*E)/h\n",
"\n",
"#results\n",
"\n",
"print \"(b) We get n = \",round(n/10**23,2),\"X 10^23.\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a) The minimum speed of the particle is 3.31 X 10^-26 m/s.\n",
"(b) We get n = 9.06 X 10^23.\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.6, page no. 203"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"import math\n",
"\n",
"#Variable declaration\n",
"\n",
"L = 0.2 #length of the box (nm)\n",
"me = 511 * 10 ** 3 #mass of electron (eV/c^2)\n",
"hc = 197.3 #(eV.nm)\n",
"\n",
"#Calculation\n",
"\n",
"E1 = math.pi ** 2 * hc**2 /(2* me * L**2)\n",
"E2 = 2**2 * E1\n",
"dE = E2-E1\n",
"lamda = hc*2*math.pi / dE\n",
"\n",
"#result\n",
"\n",
"print \"The energy required is\",round(dE,1),\"eV and the wavelength of the photon that could cause this transition is\",round(lamda),\"nm.\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The energy required is 28.2 eV and the wavelength of the photon that could cause this transition is 44.0 nm.\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.8, page no. 211"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import math\n",
"\n",
"#Variable declaration\n",
"\n",
"h = 197.3 #(eV.nm/c)\n",
"m = 511 * 10**3 #mass of electron (eV/c**2)\n",
"U = 100 #(eV)\n",
"L = 0.200 #width(nm)\n",
"\n",
"#Calculation\n",
"\n",
"d = h /math.sqrt(2*m*U)\n",
"E = math.pi**2 * h**2 /(2*m*(L+2*d)**2)\n",
"new_U = U - E\n",
"d = h/math.sqrt(2*m*new_U)\n",
"E = math.pi**2 * h**2 /(2*m*(L+2*d)**2)\n",
"\n",
"#result\n",
"\n",
"print \"The ground-state energy for the electron is\",round(E,3),\"eV.\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The ground-state energy for the electron is 6.506 eV.\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.13, page no. 217"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import math\n",
"\n",
"#Variable declaration\n",
"\n",
"m = 0.0100 #mass of the spring (kg)\n",
"K = 0.100 #force constant of spring (N/m)\n",
"Kh = 510.5 #force constant of hydrogen (N/m)\n",
"h = 6.582 * 10**-16#Planck's constant (eV.s)\n",
"mu = 8.37 * 10**-28#mass of hydrogen molecule(kg)\n",
"\n",
"#calculation\n",
"\n",
"w = math.sqrt(K / m)\n",
"dE = h * w\n",
"wh =math.sqrt(Kh / mu)\n",
"dEh = h * wh\n",
"\n",
"#results\n",
"\n",
"print \"The quantum level spacing in the spring case is\",round(dE/10**-15,2),\"X 10^-15 eV, while in case of hydrogen molecule it is\",round(dEh,3),\"eV which is easily measurable.\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The quantum level spacing in the spring case is 2.08 X 10^-15 eV, while in case of hydrogen molecule it is 0.514 eV which is easily measurable.\n"
]
}
],
"prompt_number": 10
}
],
"metadata": {}
}
]
}
|
