Quantum Mechanics
Description
This graduate-level textbook covers the essential concepts and applications of quantum mechanics. Suitable for a one-year core course, it provides a comprehensive and modern treatment, with a focus on pedagogical clarity and abundant derivations and worked examples. The text starts by reviewing the experiments that motivated the quantum revolution, then gives a concise explanation of the requisite mathematical tools, the core postulates of quantum mechanics, and the quantum version of the Noether principle relating symmetries to conserved quantities and selection rules. In addition to the usual standard topics, it covers the coherent states of the harmonic oscillator, Landau levels for a particle in a magnetic field, unbound states for Coulomb potentials, the Wigner-Eckart theorem, entanglement, the Einstein-Podolsky-Rosen problem, hidden variables theories, Bell inequalities, Aspect experiments, vibrational and rotational states of simple molecules, Bloch wavefunctions and periodic potentials, absorption and emission of light, subsystems and open systems, generalized measurements, the Lindblad equation, decoherence, the basics of quantum information, the Dirac equation, the Feynman path integral approach, and the Aharonov-Bohm effect. Exercises are included at the end of each chapter.
More details
Person
Stephen P. Martin is Professor of Physics at Northern Illinois University, where he received the university's highest award for teaching excellence. He received his PhD from the University of California at Santa Barbara, and is a Fellow of the American Physical Society. His research focuses on the frontiers of the standard model of elementary particle physics. He co-authored the textbooks Elementary Particles and Their Interactions (Springer, 2022) and From Spinors to Supersymmetry (Cambridge University Press, 2023).
Content
Introduction the Quantum Revolution.- Math Tools States Operators and Representations.- The Core Principles of Quantum Mechanics.- Canonical Variables and the Hamiltonian.- Transformations Symmetries and Conservation Laws.- Particle Moving in One Dimension.- The Harmonic Oscillator.- Angular Momentum and Its Representations.- Charged Particle in a Magnetic Field.- Examples with Spherical Symmetry.- Coulomb Potential and Hydrogen Like Atoms.- Addition of Angular Momenta.- Tensor Operators and Useful Rules They Obey.- Entanglement the EPR Problem Hidden Variables and Bell Inequalities.- Stationary State Perturbation Theory.- The Variational Method.- Fine Hyperfine and Magnetic Effects for the Hydrogen Atom.- Identical Particles and Multi Electron Atoms.- Periodic Potentials.- Simple Molecules.- Heisenberg and Interaction Representations.- Time Dependent Perturbation Theory.- Absorption and Emission of Light.- Scattering in Three Dimensions.- Subsystems Entanglement Evolution and Generalized Measurements.- Decoherence.- Invitation to Quantum Information.- Relativistic Quantum Mechanics.- Feynman Path Integral Approach.