Heisenberg’s Quantum Mechanics

This book provides a detailed account of quantum theory with a much greater emphasis on the Heisenberg equations of motion and the matrix method. No other texts have come close to discuss quantum theory in terms of depth of coverage.

The book features a deeper treatment of the fundamental concepts such as the rules of constructing quantum mechanical operators and the classical-quantal correspondence; the exact and approximate methods based on the Heisenberg equations; the determinantal approach to the scattering theory and the LSZ reduction formalism where the latter method is used to obtain the transition matrix. The uncertainty relations for a number of different observables are derived and discussed. A comprehensive chapter on the quantization of systems with nonlocalized interaction is included. Exact solvable models, and approximate techniques for solution of realistic many-body problems are also considered. The book takes a unified look in the final chapter, examining the question of measurement in quantum theory, with an introduction to the Bell’s inequalities.

Contents

1 A Brief Survey of Analytical Dynamics

2 Discovery of Matrix Mechanics

3 Mathematical Preliminaries

4 Postulates of Quantum Theory

5 Equations of Motion, Hamiltonian Operator and the Commutation Relations

6 Symmetries and Conservation Laws

7 Bound State Energies for One-Dimensional Problems

8 Exactly Solvable Potentials, Supersymmetry and Shape Invariance

9 The Two-Body Problem

10 Methods of Integration of Heisenberg’s Equations of Motion

11 Perturbation Theory

12 Other Methods of Approximation

13 Quantization of the Classical Equations of Motion with Higher Derivatives

14 Potential Scattering

15 Quantum Diffraction

16 Motion of a Charged Particle in Electromagnetic Field and Topological Quantum Effects for Neutral Particles

17 Quantum Many- Body Problem

18 Quantum Theory of Free Electromagnetic Field

19 Interaction of Radiation with Matter

20 Bell’s Inequality