Quantum Mechanics

Publication Details

Author:            Richard Fitzpatrick
Publisher: World Scientific
Publication Date: June 15, 2015
ISBN: 978-981-4689-94-6

Description

Quantum mechanics was developed during the first few decades of the twentieth century via a series of inspired guesses made by various physicists, including Planck, Einstein, Bohr, Schroedinger, Heisenberg, Pauli, and Dirac. All these scientists were trying to construct a self-consistent theory of microscopic dynamics that was compatible with experimental observations. The purpose of this book is to present quantum mechanics in a clear, concise, and systematic fashion, starting from the fundamental postulates, and developing the theory in as logical a manner as possible. Topics covered in the book include the fundamental postulates of quantum mechanics, angular momentum, time-independent and time-dependent perturbation theory, scattering theory, identical particles, and relativistic electron theory.

Table of Contents

1. Fundamental Concepts. Breakdown of Classical Physics; Photon Polarization; Fundamental Principles of Quantum Mechanics; Ket Space; Bra Space; Operators; Outer Product; Eigenvalues and Eigenvectors; Observables; Measurements; Expectation Values; Degeneracy; Compatible Observables; Uncertainty Relation; Continuous Spectra; Exercises.

2. Position and Momentum. Introduction; Poisson Brackets; Wavefunctions; Schroedinger Representation; Generalized Schroedinger Representation; Momentum Representation; Heisenberg Uncertainty Principle; Displacement Operators; Exercises.

3. Quantum Dynamics. Introduction; Schroedinger Equation of Motion; Heisenberg Equation of Motion; Ehrenfest Theorem; Schroedinger Wave Equation; Charged Particle Motion in Electromagnetic Fields; Gauge Transformations in Electromagnetism; Flux Quantization and the Aharonov-Bohm Effect; Exercises.

4. Orbital Angular Momentum. Orbital Angular Momentum; Eigenvalues of Orbital Angular Momentum; Rotation Operators; Eigenfunctions of Orbital Angular Momentum; Motion in Central Field; Energy Levels of Hydrogen Atom; Exercises.

5. Spin Angular Momentum. Introduction; Properties of Spin Angular Momentum; Wavefunction of Spin One-Half Particle; Rotation Operators in Spin Space; Magnetic Moments; Spin Precession; Pauli Two-Component Formalism; Spinor Rotation Matrices; Factorization of Spinor-Wavefunctions; Spin Greater Than One-Half Systems; Exercises.

6. Addition of Angular Momentum. Introduction; Commutation Rules; Clebsch-Gordon Coefficients; Calculation of Clebsch-Gordon Coefficients; Exercises.

7. Time-Independent Perturbation Theory. Introduction; Two-State System; Non-Degenerate Perturbation Theory; Quadratic Stark Effect; Degenerate Perturbation Theory; Linear Stark Effect; Fine Structure; Zeeman Effect; Hyperfine Structure; Exercises.

8. Time-Dependent Perturbation Theory. Introduction; General Analysis; Two-State System; Nuclear Magnetic Resonance; Dyson Series; Sudden Perturbations; Energy-Shifts and Decay-Widths; Harmonic Perturbations; Absorption and Stimulated Emission of Radiation; Spontaneous Emission of Radiation; Electric Dipole Transitions; Forbidden Transitions; Magnetic Dipole Transitions; Electric Quadrupole Transitions; Photo-Ionization; Exercises.

9. Identical Particles. Introduction; Permutation Symmetry; Spin Statistics Theorem; Two-Electron System; Helium Atom; Orthohelium and Parahelium; Variational Principle; Hydrogen Molecule Ion; Exercises.

10. Scattering Theory. Introduction; Fundamental Equations; Born Approximation; Born Expansion; Partial Waves; Optical Theorem; Determination of Phase-Shifts; Hard-Sphere Scattering; Low-Energy Scattering; Resonant Scattering; Elastic and Inelastic Scattering; Scattering of Identical Particles; Exercises.

11. Relativistic Electron Theory. Introduction; Preliminary Analysis; Dirac Equation; Lorentz Invariance of Dirac Equation; Free Electron Motion; Electron Spin; Motion in Central Field; Fine Structure of Hydrogen Energy Levels; Positron Theory; Exercises.

A. Physical Constants.

B. Solutions to Exercises.

Bibliography.

Purchase Details

This book can be purchased directly from World Scientific.

Estonian Translation

An Estonian translation of this page can be found here.
Richard Fitzpatrick