# John David Jackson

## A Course in Quantum Mechanics

1. Auflage August 2023

416 Seiten, Hardcover*Lehrbuch*

Cahn, Robert N. (Herausgeber)

**978-1-119-88038-7**

A Course in Quantum Mechanics

Unique graduate-level textbook on quantum mechanics by John David Jackson, author of the renowned Classical Electrodynamics

A Course in Quantum Mechanics is drawn directly from J. D. Jackson's detailed lecture notes and problem sets. It is edited by his 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 that are critical for understanding the material and that lead to the most important physical consequences.

Overall, the text is comprehensive and comprehensible; derivations and calculations come with clearly explained steps. More than 120 figures illustrate underlying principles, experimental apparatus, and data.

In A Course in Quantum Mechanics readers will find detailed treatments of:

* Wave mechanics of de Broglie and Schrödinger, the Klein-Gordon equation and its non-relativistic approximation, free particle probability current, expectation values.

* Schrödinger equation in momentum space, spread in time of a free-particle wave packet, density matrix, Sturm-Liouville eigenvalue problem.

* WKB formula for bound states, example of WKB with a power law potential, normalization of WKB bound state wave functions, barrier penetration with WKB.

* Rotations and angular momentum, representations, Wigner d-functions, addition of angular momenta, the Wigner-Eckart theorem.

* Time-independent perturbation theory, Stark, Zeeman, Paschen-Back effects, time-dependent perturbation theory, Fermi's Golden Rule.

* Atomic structure, helium, multiplet structure, Russell-Saunders coupling, spin-orbit interaction, Thomas-Fermi model, Hartree-Fock approximation.

* Scattering amplitude, Born approximation, allowing internal structure, inelastic scattering, optical theorem, validity criterion for the Born approximation, partial wave analysis, eikonal approximation, resonance.

* Semi-classical and quantum electromagnetism, Aharonov-Bohm effect, Lagrangian and Hamiltonian formulations, gauge invariance, quantization of the electromagnetic field, coherent states.

* Emission and absorption of radiation, dipole transitions, selection rules, Weisskopf-Wigner treatment of line breadth and level shift, Lamb shift.

* Relativistic quantum mechanics, Klein-Gordon equation, Dirac equation, two-component reduction, hole theory, Foldy-Wouthuysen transformation, Lorentz covariance, discrete symmetries, non-relativistic and relativistic Compton scattering.

1.1 Wave Mechanics of De Broglie and Schrödinger

1.2 Klein-Gordon Equation

1.3 Non-Relativistic Approximation

1.4 Free Particle Probability Current

1.5 Expectation Values

1.6 Particle in a Static, Conservative Force Field

1.7 Ehrenfest's Theorem

1.8 Schrödinger Equation in Momentum Space

1.9 Spread in Time of a Free-Particle Wave Packet

1.10 Interpretation and Application

1.11 Sturm-Liouville Eigenvalue Problem

1.12 Linear Operators on Functions

1.13 Eigenvalue Problem for a Hermitian Operator

1.14 Time-Independent Schrödinger Equation

2 General Principles of Quantum Mechanics

3 Problems in One Dimension

4 Wentzel-Kramers-Brillouin (WKB) Approximation

4.1 Solution in One Dimension

4.2 Schrödinger Equation for the Linear Potential

4.3 Connection Formulae for WKB

4.4 WKB Formula for Bound States

4.5 Example of WKB with a Power Law Potential

4.6 Normalization of WKB Bound State Wave Functions

4.7 Barrier Penetration With WKB

5 Problems in Three Dimensions

6 Rotations and Angular Momentum

7 Perturbation Methods and Applications

8 Time-Dependent Perturbation Theory

9 Atomic Structure

10 Scattering

10.1 Scattering Amplitude

10.2 Born Approximation

10.3 Allowing Internal Structure

10.4 Inelastic Scattering

10.5 Optical Theorem

10.6 Validity Criterion for the First Born Approximation

10.7 Method of Partial Waves

10.8 Behavior of the Cross Section and the Argand Diagram

10.9 Hard Sphere Scattering

10.10 Strongly Attractive Potentials and Resonance

11 Semi-Classical and Quantum Electromagnetic Field

11.1 Aharanov-Bohm Effect

11.2 Semi-Classical Radiation Theory

11.3 Scalar Field Quantization

11.4 Quantization of the Radiation Field

11.5 States of the Electromagnetic Field

11.6 Vacuum Expectation Values of E, E Times E Over Finite Volume

11.7 Classical vs Quantum Radiation

11.8 Quasi-Classical Fields and Coherent States

12 Emission and Absorption of Radiation

12.1 Matrix Elements and Rates

12.2 Dipole Transitions

12.3 Charged Particle in Central Field

12.4 Including Spin

12.5 Line Breadth and Level Shift

13 Relativistic Electron Theory

A Mathematical Tools

A.1 Integration by Parts with the Divergence Theorem

A.2 Contour Integration

A.3 Green Function for Helmholtz Equation

B Problems

C Selected Solutions

Robert N. Cahn is Senior Scientist, emeritus, at the Lawrence Berkeley National Laboratory. He has conducted research in theoretical and experimental particle physics and cosmology. The co-author, with Gerson Goldhaber, of the text Experimental Foundations of Particle Physics, he has taught physics at both the undergraduate and graduate levels.