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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Chapter 9: QUANTUM MECHANICS"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 9.14: Probability_of_electron_moving_in_1D_box.sci"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"// Scilab Code Ex9.14: Probability of electron moving in 1D box : Page-207 (2010)\n",
"a = 2e-010; // Width of 1D box, m\n",
"x1 = 0; // Position of first extreme of the box, m\n",
"x2 = 1e-010; // Position of second extreme of the box, m\n",
"P = integrate('2/a*(sin(2*%pi*x/a))^2', 'x', x1, x2); // The probability of finding the electron between x = 0 and x = 1e-010\n",
"printf('\nThe probability of finding the electron between x = 0 and x = 1e-010 = %3.1f', P);\n",
"\n",
"// Result\n",
"// The probability of finding the electron between x = 0 and x = 1e-010 = 0.5 "
]
}
,
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 9.1: De_broglie_wavelength_of_an_electron_from_accelerating_potential.sci"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"// Scilab Code Ex9.1: De-broglie wavelength of an electron from accelerating potential : Page-202 (2010)\n",
"V = 100; // Accelerating potential for electron, volt\n",
"lambda = sqrt(150/V)*1e-010; // de-Broglie wavelength of electron, m\n",
"printf('\nThe De-Broglie wavelength of electron = %4.2e m', lambda);\n",
"\n",
"// Result\n",
"// The De-Broglie wavelength of electron = 1.22e-010 m "
]
}
,
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 9.2: De_broglie_wavelength_of_an_electron_from_kinetic_energy.sci"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"// Scilab Code Ex9.2: De-broglie wavelength of an electron from kinetic energy : Page-203 (2010)\n",
"e = 1.6e-019; // Energy equivalent of 1 eV, J/eV\n",
"h = 6.626e-034; // Planck's constant, Js\n",
"m = 9.1e-031; // Mass of the electron, kg\n",
"Ek = 10; // Kinetic energy of electron, eV\n",
"// Ek = p^2/(2*m), solving for p\n",
"p = sqrt(2*m*Ek*e); // Momentum of the electron, kg-m/s\n",
"lambda = h/p ; // de-Broglie wavelength of electron from De-Broglie relation, m\n",
"printf('\nThe de-Broglie wavelength of electron = %4.2e nm', lambda/1e-009);\n",
"\n",
"// Result\n",
"// The de-Broglie wavelength of electron = 3.88e-001 nm "
]
}
,
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 9.4: Uncertainty_principle_for_position_and_momentum.sci"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"// Scilab Code Ex9.4: Uncertainty principle for position and momentum: Page-203 (2010)\n",
"h = 6.626e-034; // Planck's constant, Js\n",
"m = 9.1e-031; // Mass of the electron, kg\n",
"v = 1.1e+006; // Speed of the electron, m/s\n",
"p = m*v; // Momentum of the electron, kg-m/s\n",
"dp = 0.1/100*p; // Uncertainty in momentum, kg-m/s\n",
"h_bar = h/(2*%pi); // Reduced Planck's constant, Js\n",
"// From Heisenberg uncertainty principle,\n",
"// dx*dp = h_bar/2, solving for dx\n",
"dx = h_bar/(2*dp); // Uncertainty in position, m\n",
"printf('\nThe uncertainty in position of electron = %4.2e m', dx);\n",
"\n",
"// Result\n",
"// The uncertainty in position of electron = 5.27e-008 m "
]
}
,
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 9.5: Uncertainty_principle_for_energy_and_time.sci"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"// Scilab Code Ex9.5: Uncertainty principle for energy and time: Page-203 (2010)\n",
"e = 1.6e-019; // Energy equivalent of 1 eV, J/eV\n",
"h = 6.626e-034; // Planck's constant, Js\n",
"dt = 1e-008; // Uncertainty in time, s\n",
"h_bar = h/(2*%pi); // Reduced Planck's constant, Js\n",
"// From Heisenberg uncertainty principle,\n",
"// dE*dt = h_bar/2, solving for dE\n",
"dE = h_bar/(2*dt*e); // Uncertainty in energy of the excited state, m\n",
"printf('\nThe uncertainty in energy of the excited state = %4.2e eV', dE);\n",
"\n",
"// Result\n",
"// The uncertainty in energy of the excited state = 3.30e-008 eV"
]
}
,
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 9.6: Width_of_spectral_line_from_Uncertainty_principle.sci"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"// Scilab Code Ex9.6: Width of spectral line from Uncertainty principle: Page-204 (2010)\n",
"c = 3e+008; // Speed of light, m/s\n",
"dt = 1e-008; // Average lifetime, s\n",
"lambda = 400e-009; // 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_lambda = lambda^2/(4*%pi*c*dt); // Width of spectral line, m\n",
"printf('\nThe width of spectral line = %4.2e m', d_lambda);\n",
"\n",
"// Result\n",
"// The width of spectral line = 4.24e-015 m "
]
}
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"text": "MetaKernel Magics",
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