In diesem Buch werden die grundlegenden Begriffe und Erscheinungen der Quantenmechanik eingeführt und visualisiert. Computergrafiken dienen zur Veranschaulichung der zunächst ungewohnt abstrakten Begriffe dieses Gebiets. Dabei werden insbesondere Vergleiche mit der klassischen Mechanik und der Wellenoptik herangezogen. Grafiken vieler Beispiele helfen dabei, eine Intuition auch für quantenmechanische Vorgänge zu vermitteln. Mehr als 80 computergenerierte Videos zum Buch sind in einem YouTube-Kanal zusammengefasst und über QR-Codes im Buch leicht einzusehen. Studierenden der Physik sowie…mehr
In diesem Buch werden die grundlegenden Begriffe und Erscheinungen der Quantenmechanik eingeführt und visualisiert. Computergrafiken dienen zur Veranschaulichung der zunächst ungewohnt abstrakten Begriffe dieses Gebiets. Dabei werden insbesondere Vergleiche mit der klassischen Mechanik und der Wellenoptik herangezogen. Grafiken vieler Beispiele helfen dabei, eine Intuition auch für quantenmechanische Vorgänge zu vermitteln. Mehr als 80 computergenerierte Videos zum Buch sind in einem YouTube-Kanal zusammengefasst und über QR-Codes im Buch leicht einzusehen. Studierenden der Physik sowie Lehramtsstudierenden der Physik oder Chemie werden folgende spannende Themen erklärt: Lichtwellen, Materiewellen, Wellenpakete, Schrödinger-Gleichung, WahrscheinlichkeitsinterpretationQuantenmechanik in einer Dimension: Streuung, gebundene Zustände, Bewegung im Potential, kohärente und gestauchte Zustände, QuantilbewegungZweiteilchenzustände: unterscheidbare und ununterscheidbare TeilchenQuantenmechanik in drei Dimensionen: Drehimpuls, Streuamplitude, Streuquerschnitt, Resonanzstreuung, Wasserstoffatom, KeplerbewegungHybridisierungSpin und magnetische ResonanzExperimentelle Beispiele aus Atom-, Kern-, Teilchen- und FestkörperphysikEinfache Aspekte der Struktur der Quantenmechanik
Siegmund Brandt ist emeritierter Professor der Physik und Hans Dieter Dahmen ist emeritierter Professor der Theoretischen Physik, beide an der Universität Siegen. Ihre Forschungsgebiete waren die experimentelle bzw. theoretische Physik der Elementarteilchen. Sie sind Autoren bzw. Koautoren von Lehrbüchern, die in zehn Sprachen erschienen sind.
Inhaltsangabe
1 Introduction.- 1.1 The Photoelectric Effect.- 1.2 The Compton Effect.- 1.3 The Diffraction of Electrons.- 1.4 The Stern-Gerlach Experiment.- 2 Light Waves, Photons.- 2.1 Harmonic Plane Waves, Phase Velocity.- 2.2 Light Wave Incident on a Glass Surface.- 2.3 Light Wave Traveling through a Glass Plate.- 2.4 Free Wave Packet.- 2.5 Wave Packet Incident on a Glass Surface.- 2.6 Wave Packet Traveling through a Glass Plate.- 2.7 The Photon.- 3 Probability Waves of Matter.- 3.1 de Broglie Waves.- 3.2 Wave packet, Dispersion.- 3.3 Probability Interpretation, Uncertainty Principle.- 3.4 The Schrödinger Equation.- 3.5 Bivariate Gaussian Probability Density.- 3.6 Comparison with a Classical Statistical Description.- 4 Solution of the Schrödinger Equation in One Dimension.- 4.1 Separation of Time and Space Coordinates, Stationary Solutions.- 4.2 Stationary Scattering Solutions: Piecewise Constant Potential.- 4.3 Stationary Scattering Solutions: Linear Potentials.- 4.4 Stationary Bound States.- 5 One-Dimensional Quantum Mechanics: Scattering by a Potential.- 5.1 Sudden Acceleration and Deceleration of a Particle.- 5.2 Sudden Deceleration of a Classical Phase-Space Distribution.- 5.3 Tunnel Effect.- 5.4 Excitation and Decay of Metastable States.- 5.5 Stationary States of Sharp Momentum.- 5.6 Free Fall of a Body.- 6 One-Dimensional Quantum Mechanics: Motion within a Potential, Stationary Bound States.- 6.1 Spectrum of a Deep Square Well.- 6.2 Particle Motion in a Deep Square Well.- 6.3 Spectrum of the Harmonic-Oscillator Potential.- 6.4 Harmonic Particle Motion.- 6.5 Harmonic Motion of a Classical Phase-Space Distribution.- 6.6 Spectra of Square-Well Potentials of Finite Depths.- 6.7 Periodic Potentials, Band Spectra.- 7 Quantile Motion in One Dimension.- 7.1 Quantile Motion and Tunneling.- 7.2 Probability Current, Continuity Equation.- 7.3 Probability Current Densities of Simple Examples.- 7.4 Differential Equation of the Quantile Trajectory.- 7.5 Error Function.- 7.6 Quantile Trajectories for Simple Examples.- 7.7 Relation to Bohm's Equation of Motion.- 8 Coupled Harmonic Oscillators: Distinguishable Particles.- 8.1 The Two-Particle Wave Function.- 8.2 Coupled Harmonic Oscillators.- 8.3 Stationary States.- 9 Coupled Harmonic Oscillators: Indistinguishable Particles.- 9.1 The Two-Particle Wave Function for Indistinguishable Particles.- 9.2 Stationary States.- 9.3 Motion of Wave Packets.- 9.4 Indistinguishable Particles from a Classical Point of View.- 10 Wave Packet in Three Dimensions.- 10.1 Momentum.- 10.2 Quantile Motion, Probability Transport.- 10.3 Angular Momentum, Spherical Harmonics.- 10.4 Means and Variances of the Components of Angular Momentum.- 10.5 Interpretation of the Eigenfunctions of Angular Momentum.- 10.6 Schrödinger Equation.- 10.7 Solution of the Schrödinger Equation of Free Motion.- 10.8 Spherical Bessel Functions.- 10.9 Harmonic Plane Wave in Angular-Momentum Representationo.- 10.10 Free Wave Packet and Partial-Wave Decomposition.- 11 Solution of the Schrödinger Equation in Three Dimensions.- 11.1 Stationary Scattering Solutions.- 11.2 Stationary Bound States.- 12 Three-Dimensional Quantum Mechanics: Scattering by a Potential.- 12.1 Diffraction of a Harmonic Plane Wave. Partial Waves.- 12.2 Scattered Wave and Scattering Cross Section.- 12.3 Scattering Phase and Amplitude, Unitarity, Argand Diagrams.- 13 Three-Dimensional Quantum Mechanics: Bound States.- 13.1 Bound States in a Spherical Square-Well Potential.- 13.2 Bound States of the Spherically Symmetric Harmonic Oscillator.- 13.3 Harmonic Particle Motion in Three Dimensions.- 13.4 The Hydrogen Atom.- 13.5 Kepler Motion in Quantum Mechanics.- 14 Three-Dimensional Quantum Mechanics: Resonance Scattering.- 14.1 Scattering by Attractive Potentials.- 14.2 Resonance Scattering.- 14.3 Phase-Shift Analysis.- 14.4 Bound States and Resonances.- 14.5 Resonance Scattering by a Repulsive Shell.- 15 Coulomb Scattering.- 15.1 Stationary Solutions.- 15.2 Hyperbolic Kepler Motion: Scattering of a Gaussian Wave Packet by a Coulomb Potential.- 16 Spin.- 16.1 Spin States, Operators and Eigenvalues.- 16.2 Directional Distribution of Spin.- 16.3 Motion of Magnetic Moments in a Magnetic Field. Pauli Equation.- 16.4 Magnetic Resonance. Rabi's Formula.- 16.5 Magnetic Resonance in a Rotating Frame of Reference.- 17 Examples from Experiment.- 17.1 Scattering of Atoms, Electrons, Neutrons, and Pions.- 17.2 Spectra of Bound States in Atoms, Nuclei, and Crystals.- 17.3 Shell-Model Classification of Atoms and Nuclei, and Particles.- 17.4 Resonance Scattering off Molecules, Atoms, Nuclei, and particles.- 17.5 Phase-Shift Analysis in Nuclear and Particle Physics.- 17.6 Classification of Resonances on Regge Trajectories.- 17.7 Radioactive Nuclei as Metastable States.- 17.8 Magnetic-Resonance Experiments.- A Simple Aspects of the Structure of Quantum Mechanics.- A.1 Wave Mechanics.- A.2 Matrix Mechanics in an Infinite Vector Space.- A.3 Matrix Representation of the Harmonic Oscillator.- A.4 Time-Dependent Schrödinger Equation.- A.5 Probability Interpretation.- B Two-Level System.- C Analyzing Amplitude.- C.1 Classical Considerations: Phase-Space Analysis.- C.2 Analyzing Amplitude: Free Particle.- C.3 Analyzing Amplitude: General Case.- C.4 Analyzing Amplitude: Harmonic Oscillator.- D Wigner Distribution.- E Gamma Function.- F Bessel Functions and Airy Functions.- G Poisson Distribution.
1 Introduction.- 1.1 The Photoelectric Effect.- 1.2 The Compton Effect.- 1.3 The Diffraction of Electrons.- 1.4 The Stern-Gerlach Experiment.- 2 Light Waves, Photons.- 2.1 Harmonic Plane Waves, Phase Velocity.- 2.2 Light Wave Incident on a Glass Surface.- 2.3 Light Wave Traveling through a Glass Plate.- 2.4 Free Wave Packet.- 2.5 Wave Packet Incident on a Glass Surface.- 2.6 Wave Packet Traveling through a Glass Plate.- 2.7 The Photon.- 3 Probability Waves of Matter.- 3.1 de Broglie Waves.- 3.2 Wave packet, Dispersion.- 3.3 Probability Interpretation, Uncertainty Principle.- 3.4 The Schrödinger Equation.- 3.5 Bivariate Gaussian Probability Density.- 3.6 Comparison with a Classical Statistical Description.- 4 Solution of the Schrödinger Equation in One Dimension.- 4.1 Separation of Time and Space Coordinates, Stationary Solutions.- 4.2 Stationary Scattering Solutions: Piecewise Constant Potential.- 4.3 Stationary Scattering Solutions: Linear Potentials.- 4.4 Stationary Bound States.- 5 One-Dimensional Quantum Mechanics: Scattering by a Potential.- 5.1 Sudden Acceleration and Deceleration of a Particle.- 5.2 Sudden Deceleration of a Classical Phase-Space Distribution.- 5.3 Tunnel Effect.- 5.4 Excitation and Decay of Metastable States.- 5.5 Stationary States of Sharp Momentum.- 5.6 Free Fall of a Body.- 6 One-Dimensional Quantum Mechanics: Motion within a Potential, Stationary Bound States.- 6.1 Spectrum of a Deep Square Well.- 6.2 Particle Motion in a Deep Square Well.- 6.3 Spectrum of the Harmonic-Oscillator Potential.- 6.4 Harmonic Particle Motion.- 6.5 Harmonic Motion of a Classical Phase-Space Distribution.- 6.6 Spectra of Square-Well Potentials of Finite Depths.- 6.7 Periodic Potentials, Band Spectra.- 7 Quantile Motion in One Dimension.- 7.1 Quantile Motion and Tunneling.- 7.2 Probability Current, Continuity Equation.- 7.3 Probability Current Densities of Simple Examples.- 7.4 Differential Equation of the Quantile Trajectory.- 7.5 Error Function.- 7.6 Quantile Trajectories for Simple Examples.- 7.7 Relation to Bohm's Equation of Motion.- 8 Coupled Harmonic Oscillators: Distinguishable Particles.- 8.1 The Two-Particle Wave Function.- 8.2 Coupled Harmonic Oscillators.- 8.3 Stationary States.- 9 Coupled Harmonic Oscillators: Indistinguishable Particles.- 9.1 The Two-Particle Wave Function for Indistinguishable Particles.- 9.2 Stationary States.- 9.3 Motion of Wave Packets.- 9.4 Indistinguishable Particles from a Classical Point of View.- 10 Wave Packet in Three Dimensions.- 10.1 Momentum.- 10.2 Quantile Motion, Probability Transport.- 10.3 Angular Momentum, Spherical Harmonics.- 10.4 Means and Variances of the Components of Angular Momentum.- 10.5 Interpretation of the Eigenfunctions of Angular Momentum.- 10.6 Schrödinger Equation.- 10.7 Solution of the Schrödinger Equation of Free Motion.- 10.8 Spherical Bessel Functions.- 10.9 Harmonic Plane Wave in Angular-Momentum Representationo.- 10.10 Free Wave Packet and Partial-Wave Decomposition.- 11 Solution of the Schrödinger Equation in Three Dimensions.- 11.1 Stationary Scattering Solutions.- 11.2 Stationary Bound States.- 12 Three-Dimensional Quantum Mechanics: Scattering by a Potential.- 12.1 Diffraction of a Harmonic Plane Wave. Partial Waves.- 12.2 Scattered Wave and Scattering Cross Section.- 12.3 Scattering Phase and Amplitude, Unitarity, Argand Diagrams.- 13 Three-Dimensional Quantum Mechanics: Bound States.- 13.1 Bound States in a Spherical Square-Well Potential.- 13.2 Bound States of the Spherically Symmetric Harmonic Oscillator.- 13.3 Harmonic Particle Motion in Three Dimensions.- 13.4 The Hydrogen Atom.- 13.5 Kepler Motion in Quantum Mechanics.- 14 Three-Dimensional Quantum Mechanics: Resonance Scattering.- 14.1 Scattering by Attractive Potentials.- 14.2 Resonance Scattering.- 14.3 Phase-Shift Analysis.- 14.4 Bound States and Resonances.- 14.5 Resonance Scattering by a Repulsive Shell.- 15 Coulomb Scattering.- 15.1 Stationary Solutions.- 15.2 Hyperbolic Kepler Motion: Scattering of a Gaussian Wave Packet by a Coulomb Potential.- 16 Spin.- 16.1 Spin States, Operators and Eigenvalues.- 16.2 Directional Distribution of Spin.- 16.3 Motion of Magnetic Moments in a Magnetic Field. Pauli Equation.- 16.4 Magnetic Resonance. Rabi's Formula.- 16.5 Magnetic Resonance in a Rotating Frame of Reference.- 17 Examples from Experiment.- 17.1 Scattering of Atoms, Electrons, Neutrons, and Pions.- 17.2 Spectra of Bound States in Atoms, Nuclei, and Crystals.- 17.3 Shell-Model Classification of Atoms and Nuclei, and Particles.- 17.4 Resonance Scattering off Molecules, Atoms, Nuclei, and particles.- 17.5 Phase-Shift Analysis in Nuclear and Particle Physics.- 17.6 Classification of Resonances on Regge Trajectories.- 17.7 Radioactive Nuclei as Metastable States.- 17.8 Magnetic-Resonance Experiments.- A Simple Aspects of the Structure of Quantum Mechanics.- A.1 Wave Mechanics.- A.2 Matrix Mechanics in an Infinite Vector Space.- A.3 Matrix Representation of the Harmonic Oscillator.- A.4 Time-Dependent Schrödinger Equation.- A.5 Probability Interpretation.- B Two-Level System.- C Analyzing Amplitude.- C.1 Classical Considerations: Phase-Space Analysis.- C.2 Analyzing Amplitude: Free Particle.- C.3 Analyzing Amplitude: General Case.- C.4 Analyzing Amplitude: Harmonic Oscillator.- D Wigner Distribution.- E Gamma Function.- F Bessel Functions and Airy Functions.- G Poisson Distribution.
Rezensionen
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