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diff --git a/Modern_Physics_by_R_A_Serway/6-Quantum_mechanics_in_one_dimension.ipynb b/Modern_Physics_by_R_A_Serway/6-Quantum_mechanics_in_one_dimension.ipynb new file mode 100644 index 0000000..ef78190 --- /dev/null +++ b/Modern_Physics_by_R_A_Serway/6-Quantum_mechanics_in_one_dimension.ipynb @@ -0,0 +1,360 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 6: Quantum mechanics in one dimension" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.12: The_quantum_oscillator_in_nonclassical_region.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab code Ex6.12: Pg 214 (2005)\n", +"clc; clear;\n", +"P = 2/sqrt(%pi)*integrate('exp(-z^2)', 'z', 1, 100); // Probability that the quantum oscillator in its ground state will be found in the nonclassical region\n", +"printf('\nThe probability that the quantum oscillator in its ground state will be found in the nonclassical region = %5.3f', P);\n", +"\n", +"// Result\n", +"// The probability that the quantum oscillator in its ground state will be found in the nonclassical region = 0.157 " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.13: Quantization_of_vibrational_energy.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab code Ex6.13: Pg 211 (2005)\n", +"clc; clear;\n", +"h_cross = 6.582e-016; // Reduced Planck's constant, eV-s\n", +"// For spring-mass system\n", +"K = 0.100; // Force constant of the spring-mass system, N/m\n", +"m = 0.0100; // Mass attached to the spring, kg\n", +"omega = sqrt(K/m); // Angular frequency of oscillations, rad/s\n", +"delta_E = h_cross*omega; // Energy spacing between quantum levels, eV\n", +"printf('\nThe energy spacing between quantum levels for spring-mass system = %4.2e eV\nwhich is far below present limits of detection', delta_E);\n", +"// For vibrating hydrogen molecule\n", +"K = 510.5; // Force constant of the hydrogen molecule system, N/m\n", +"mu = 8.37e-028; // Reduced mass of the hydrogen molecule, kg\n", +"omega = sqrt(K/mu); // Angular frequency of oscillations, rad/s\n", +"delta_E = h_cross*omega; // Energy spacing between quantum levels, eV\n", +"printf('\nThe energy spacing between quantum levels for hydrogen molecule = %5.3f eV\nwhich can be measured easily', delta_E);\n", +"\n", +"// Result\n", +"// The energy spacing between quantum levels for spring-mass system = 2.08e-15 eV\n", +"// which is far below present limits of detection\n", +"// The energy spacing between quantum levels for hydrogen molecule = 0.514 eV\n", +"// which can be measured easily " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.14: Standard_Deviations_from_Averages.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab code Ex6.14: Pg 219 (2005)\n", +"clc; clear;\n", +"x = [2.5, 3.7, 1.4, 7.9, 6.2, 5.4, 8.0, 6.4, 4.1, 5.4, 7.0, 3.3, 4.2, 8.8, 6.2, 7.1, 5.4, 5.3]; // Data entries\n", +"sum_x = 0; // Initialize the accumulator\n", +"sum_x_sq = 0; // Initialize the second accumulator\n", +"N = 18; // Total number of data points\n", +"for i = 1:1:N\n", +" sum_x = sum_x + x(i); // Sum of data\n", +" sum_x_sq = sum_x_sq + x(i)^2; // Sum of square of data\n", +"end\n", +"x_av = sum_x/N; // Average of data\n", +"x_sq_av = sum_x_sq/N; // Mean square value\n", +"sigma = sqrt(x_sq_av-x_av^2); // Standard deviation from averages\n", +"printf('\nThe standard deviation from averages = %4.2f', sigma);\n", +"\n", +"\n", +"// Result\n", +"// The standard deviation from averages = 1.93 " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.15: Location_of_a_particle_in_the_box.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab code Ex6.15: Pg 219 (2005)\n", +"clc; clear;\n", +"L = 1; // For simplicity assume length of the box to be unity, unit\n", +"x_av = 2*L/%pi^2*integrate('theta*sin(theta)^2', 'theta', 0, %pi); // Average value of x\n", +"x_sq_av = L^2/%pi^3*(integrate('theta^2', 'theta', 0, %pi)-integrate('theta^2*cos(2*theta)', 'theta', 0, %pi)); // Average value of x square\n", +"delta_x = sqrt(x_sq_av - x_av^2); // Uncertainty in the position for this particle, unit\n", +"printf('\nThe average position of the particle in the box = L/%1d', x_av*4);\n", +"printf('\nThe uncertainty in the position for the particle = %5.3fL', delta_x);\n", +"\n", +"// Result\n", +"// The average position of the particle in the box = L/2\n", +"// The uncertainty in the position for the particle = 0.181L " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.2: Probability_from_wave_function.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab code Ex6.2: Pg 193 (2005)\n", +"clc; clear;\n", +"x0 = 1; // For simplicity assume x0 = 1\n", +"C = 1/sqrt(x0); // Normalization constant\n", +"P = 2*C^2*integrate('exp(-2*x/x0)', 'x', 0, x0);\n", +"printf('\nThe probability that the particle will be found in the interval -x0 <= x <= x0 is %6.4f or %4.1f percent', P, P*100);\n", +"\n", +"// Result\n", +"// The probability that the particle will be found in the interval -x0 <= x <= x0 is 0.8647 " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.4: Dispersion_of_matter_waves.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab code Ex6.4: Pg 197 (2005)\n", +"clc; clear;\n", +"delta_x0 = 1e-010; // Initial width of the localized space, m\n", +"delta_xt = 10*delta_x0; // Final width at which the wave packet is dispersed, m\n", +"h_cross = 1.055e-034; // Reduced Planck's constant, Js\n", +"m = 9.11e-031; // Mass of the electron, kg\n", +"// From Dispersion relation, delta_xt^2 - delta_x0^2 = sqrt(h_cross*t/(2*m*deltax0)^2), solving for t\n", +"t = 2*m*sqrt(delta_xt^2 - delta_x0^2)*delta_x0/h_cross; // Time which elapses before delocalization\n", +"printf('\nThe time which elapses before the localization of electron destroys = %3.1e s', t);\n", +"m = 1e-03; // Mass of marble, kg\n", +"delta_x0 = 1e-004; // Initial width of the localized space, m\n", +"delta_xt = 10*delta_x0; // Final width at which the wave packet is dispersed, m\n", +"t = 2*m*sqrt(delta_xt^2 - delta_x0^2)*delta_x0/h_cross; // Time which elapses before delocalization\n", +"printf('\nThe time which elapses before the localization of marble destroys = %3.1e s', t);\n", +"printf('\nFor all the practical purposes, the marble will remain localized for ever');\n", +"// Result\n", +"// \n", +"\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.5: Energy_Quantization_for_Macroscopic_Object.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab code Ex6.5: Pg 202 (2005)\n", +"clc; clear;\n", +"h = 6.626e-034; // Planck's constant, Js\n", +"m = 1e-06; // Mass of the object, kg\n", +"n = 1; // Quantum number for minimum energy level\n", +"L = 1e-02; // Distance between two rigid walls, m\n", +"E1 = n^2*h^2/(8*m*L^2); // Minimum energy of the object, J\n", +"v1 = sqrt(2*E1/m); // Minimum speed of the object, m/s\n", +"v = 3.00e-02; // Given speed of the objct, m/s\n", +"E = 1/2*m*v^2; // Energy of the object for given speed, J\n", +"n = sqrt(8*m*L^2*E)/h; // Quantum number corresponding to the given speed\n", +"printf('\nThe minimum speed of the object = %4.2e m/s', v1);\n", +"printf('\nThe quantum number corresponding to the speed of %4.2e m/s is n = %4.2e', v1, n);\n", +"\n", +"// Result\n", +"// The minimum speed of the object = 3.31e-26 m/s\n", +"// The quantum number corresponding to the speed of 3.31e-26 m/s is n = 9.06e+23 " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.6: Model_of_an_Atom.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab code Ex6.6: Pg 203 (2005)\n", +"clc; clear;\n", +"c = 1; // Assume speed of light to be unity, m/s\n", +"h_cross = 197.3; // Reduced Planck's constant, eV.nm/c^2\n", +"m_e = 511e+03; // Mass of an electron, eV/c^2\n", +"L = 0.200; // Length of the box, nm\n", +"E1 = %pi^2*(h_cross/c)^2/(2*m_e*L^2); // Ground state energy of atomic electron, eV\n", +"E2 = 2^2*E1; // Excited state energy of the atomic electron, eV\n", +"delta_E = E2- E1; // Energy that must be applied to the electron to raise it from ground to the first excited state, eV\n", +"h = 2*%pi*h_cross; // Planck's constant, Js\n", +"lambda = h*c/delta_E; // Wavelength of the photon to cause the electron transition, nm\n", +"printf('\nThe energy that must be applied to the electron to raise it from ground to the first excited state = %4.1f eV', delta_E);\n", +"printf('\nThe wavelength of the photon to cause this electron transition = %4.1f nm', lambda);\n", +"printf('\nThis wavelength is in the far ultraviolet region.');\n", +"\n", +"// Result\n", +"// The energy that must be applied to the electron to raise it from ground to the first excited state = 28.2 eV\n", +"// The wavelength of the photon to cause this electron transition = 44.0 nm\n", +"// This wavelength is in the far ultraviolet region. " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.7: Probabilities_for_a_particle_in_a_Box.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab code Ex6.7: Pg 205 (2005)\n", +"clc; clear;\n", +"L = 1; // For simplicity assume length of finite square well to be unity, m\n", +"P = 2/L*integrate('sin(%pi*x/L)^2', 'x', L/4, 3*L/4); // Probability that the particle will be found in the middle half of the well\n", +"printf('\nThe probability that the particle will be found in the middle half of the well = %5.3f', P);\n", +"\n", +"// Result\n", +"// The probability that the particle will be found in the middle half of the well = 0.818" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.8: Ground_state_energy_of_an_electron_confined_to_a_potential_well.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"\n", +"// Scilab code Ex6.8: Pg 211 (2005)\n", +"clc; clear;\n", +"c = 1; // Assume speed of light to be unity, m/s\n", +"L = 0.200; // Width of the potential well, nm\n", +"h_cross = 197.3; // Reduced Planck's constant, eV.nm/c^2\n", +"m = 511e+03; // Mass of an electron, eV/c^2\n", +"U = 100; // Height of potential well, eV\n", +"delta = h_cross/sqrt(2*m*U); // Decay length of electron, nm\n", +"L = L + 2*delta; // Effective length of the infinite potential well, nm\n", +"E = %pi^2*(h_cross/c)^2/(2*m*L^2); // Ground state energy of the electron with effective length, eV\n", +"U = U - E; // New potential energy, eV\n", +"delta = h_cross/sqrt(2*m*U); // New decay length of electron, nm\n", +"printf('\nThe ground state energy of an electron confined to the potential well = %4.2f eV', E);\n", +"printf('\nThe new decay length of the electron = %6.4f nm', delta);\n", +"\n", +"// Result\n", +"// The ground state energy of an electron confined to the potential well = 6.58 eV \n", +"// The new decay length of the electron = 0.0202 nm " + ] + } +], +"metadata": { + "kernelspec": { + "display_name": "Scilab", + "language": "scilab", + "name": "scilab" + }, + "language_info": { + "file_extension": ".sce", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "scilab", + "version": "0.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} |