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Quantum Mechanics on the Personal Computer

Erscheinungsjahr: 2014
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ISBN/EAN: 9783642786570
Sprache: Englisch
Auflage: 3. Auflage

Beschreibung

Inhaltsangabe1. Introduction.- 1.1 Interquanta.- 1.2 The Structure of this Book.- 1.3 The Demonstrations.- 1.4 The Computer Laboratory.- 1.5 Literature.- 2. Free Particle Motion in One Dimension.- 2.1 Physical Concepts.- 2.1.1 Planck's Constant. Schrödinger's Equation for a Free Particle.- 2.1.2 The Wave Packet. Group Velocity. Normalization.- 2.1.3 Analogies in Optics.- 2.2 A First Session with the Computer.- 2.2.1 Starting IQ.- 2.2.2 An Automatic Demonstration.- 2.2.3 A First Dialogue.- 2.2.4 A Little Systematics.- 2.3 The Time Development of a Gaussian Wave Packet.- 2.4 The Spectral Function of a Gaussian Wave Packet.- 2.5 The Wave Packet as a Sum of Harmonic Waves.- 2.6 Exercises.- 3. Bound States in One Dimension.- 3.1 Physical Concepts.- 3.1.1 Schrödinger's Equation with a Potential. Eigenfunctions. Eigenvalues.- 3.1.2 Normalization. Discrete Spectra. Orthonormality.- 3.1.3 The Infinitely Deep Square-Well Potential.- 3.1.4 The Harmonic Oscillator.- 3.1.5 The Step Potential.- 3.1.6 Time-Dependent Solutions.- 3.1.7 Harmonic Particle Motion. Coherent States. Squeezed States.- 3.1.8 Particle Motion in a Deep Square Well.- 3.2 Eigenstates in the Infinitely Deep Square-Well Potential and in the Harmonic-Oscillator Potential.- 3.3 Eigenstates in the Step Potential.- 3.4 Harmonic Particle Motion.- 3.5 Particle Motion in the Infinitely Deep Square-Well Potential.- 3.6 Exercises.- 4. Scattering in One Dimension.- 4.1 Physical Concepts.- 4.1.1 Stationary Scattering States. Continuum Eigenstates and Eigenvalues. Continuous Spectra.- 4.1.2 Time-Dependent Solutions of the Schrödinger Equation.- 4.1.3 Right-Moving and Left-Moving Stationary Wavesof a Free Particle.- 4.1.4 Orthogonality and Continuum Normalization of Stationary Waves of a Free Particle. Completeness.- 4.1.5 Boundary Conditions for Stationary Scattering Solutions in Step Potentials.- 4.1.6 Stationary Scattering Solutions in Step Potentials.- 4.1.7 Constituent Waves.- 4.1.8 Normalization of Continuum Eigenstates.- 4.1.9 Harmonic Waves in a Step Potential.- 4.1.10 Time-Dependent Scattering Solutions in a Step Potential.- 4.1.11 Transmission and Reflection. Unitarity. The Argand Diagram.- 4.1.12 The Tunnel Effect.- 4.1.13 Resonances.- 4.1.14 Phase Shifts upon Reflection at a Steep Rise or Deep Fall of the Potential.- 4.1.15 Transmission Resonances upon Reflection at "More- and Less-Dense Media".- 4.1.16 The Quantum-Well Device and the Quantum-Effect Device.- 4.2 Stationary Scattering States in the Step Potential.- 4.3 Scattering of a Harmonic Wave by the Step Potential.- 4.4 Scattering of a Wave Packet by the Step Potential.- 4.5 Transmission and Reflection. The Argand Diagram.- 4.6 Exercises.- 4.7 Analogies in Optics.- 4.8 Reflection and Refraction of Stationary Electromagnetic Waves.- 4.9 Reflection and Refraction of a Harmonic Light Wave.- 4.10 Scattering of a Wave Packet of Light.- 4.11 Transmission, Reflection and Argand Diagram for a Light Wave.- 4.12 Exercises.- 5. A Two-Particle System: Coupled Harmonic Oscillators.- 5.1 Physical Concepts.- 5.1.1 The Two-Particle System.- 5.1.2 Initial Condition for Distinguishable Particles.- 5.1.3 Time-Dependent Wave Functions and Probability Distributions for Distinguishable Particles.- 5.1.4 Marginal Distributions for Distinguishable Particles.- 5.1.5 Wave Functions for Indistinguishable Particles. Symmetrization for Bosons. Antisymmetrization for Fermions.- 5.1.6 Marginal Distributions of the Probability Densities of Bosons and Fermions.- 5.1.7 Normal Oscillations.- 5.2 Stationary States.- 5.3 Time Dependence of Global Quantities.- 5.4 Joint Probability Densities.- 5.5 Marginal Distributions.- 5.6 Exercises.- 6. Free Particle Motion in Three Dimensions.- 6.1 Physical Concepts.- 6.1.1 The Schrödinger Equation of a Free Particle in Three Dimensions. The Momentum Operator.- 6.1.2 The Wave Packet. Group Velocity. Normalization. The Probability Ellipsoid.- 6.1.3 Angular Momentum. Spherical Harmonics.- 6.1.4 The Stationary Schrödinger Equation in

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