John David Jackson: A Course in Quantum Mechanics (Hardcover)

Jackson's posthumously published textbook, A Course on Quantum Mechanics, covers quantum mechanics at an advanced level, presenting fundamental principles and techniques including the Schrödinger and Heisenberg representations, angular momentum, perturbation theory, scattering, quantum theory of radiation, and relativistic quantum mechanics. Particular attention is devoted to the WKB and eikonal approximations, which can be applied to a broad range of physical circumstances. An especially thorough treatment is given to atomic physics. The principles of quantum mechanics are illustrated in applications to atomic, nuclear, particle, and condensed matter physics, demonstrating that quantum mechanics provides a quantitative understanding of matter and light.

The book is drawn directly from Jackson’s detailed lecture notes and problem sets. It is edited by colleague and former student Robert N. Cahn, who has taken care to preserve Jackson’s unique style. The textbook is notable for its original problems focused on real applications, with many addressing published data in accompanying tables and figures. Solutions are provided for problems whose content is critical for understanding the material and whose physical consequences are the most important.

Overall, the text is comprehensive and comprehensible. Particular care is taken to present in detailed the steps in each derivation or calculation. More than 120 figures are included to illustrate both underlying principles, experimental apparatus, and data.

In A Course on Quantum Mechanics, readers can expect to find detailed information on:

1. Wave mechanics of De Broglie and Schrödinger, the Klein-Gordon equation, non-relativistic approximation, free particle probability current, and expectation values
2. Schrödinger Equation in momentum space, spread in time of a free-particle wave packet, density matrix, and Sturm-Liouville Eigenvalue problem
3. WKB formula for bound states, example of WKB with a power law potential, normalization of WKB bound state wave functions, and barrier penetration with WKB.
4. Rotations and angular momentum, representations, Wigner d-functions, addition of angular momenta, and the Wigner-Eckart theorem.
5. Time-independent perturbation theory, Stark, Zeeman, Paschen-Back effects, time-dependent perturbation theory, and Fermi’s Golden Rule.
6. Atomic structure, helium, multiplet structure, Russell-Saunders coupling, spin-orbit interaction, Thomas-Fermi model, and the Hartree-Fock approximation.
7. Scattering amplitude, Born approximation, allowing internal structure, inelastic scattering, optical theorem, and validity criterion for the first Born approximation, partial wave analysis, eikonal approximation, resonance.
8. Semi-classical and quantum electromagnetism, Aharonov-Bohm effect, Lagrangian and Hamiltonian formulations, gauge invariance, quantization of the electromagnetic field, and coherent states.
9. Emission and absorption of radiation, dipole transitions, selection rules, Weisskopf-Wigner treatment of line breadth and level shift, and the Lamb shift.
10. Relativistic quantum mechanics, Klein-Gordon equation, Dirac equation, two-component reduction, hole theory, Foldy-Wouthuysen transformation, Lorentz covariance, discrete symmetries, and non-relativistic and relativistic Compton scattering. The textbook follows the unique—demanding!— style of Jackson's Classical Electrodynamics, A Course on Quantum Mechanics is an advanced level textbook, highly suitable for ambitious graduate students and their instructors, and containing novel problems with detailed solutions to aid in gaining a solid understanding of the subject.