Quantum Mechanics

Author:            Richard Fitzpatrick

Publisher:         World Scientific

Publication Date:  June 15, 2015

ISBN:              978-981-4689-94-6

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.

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.