Berman P.R. Introductory Quantum Mechanics: A Traditional Approach Emphasizing Connections with Classical Physics

Springer International Publishing AG, 2018. — 641 p. — (UNITEXT for Physics). — ISBN: 978-3-319-68596-0.This book presents a basic introduction to quantum mechanics. Depending on the choice of topics, it can be used for a one-semester or two-semester course. An attempt has been made to anticipate the conceptual problems students encounter when they first study quantum mechanics. Wherever possible, examples are given to illustrate the underlying physics associated with the mathematical equations of quantum mechanics. To this end, connections are made with corresponding phenomena in classical mechanics and electromagnetism. The problems at the end of each chapter are intended to help students master the course material and to explore more advanced topics. Many calculations exploit the extraordinary capabilities of computer programs such as Mathematica, MatLAB, and Maple. Students are urged to use these programs, just as they had been urged to use calculators in the past. The treatment of various topics is rather complete, in that most steps in derivations are included. Several of the chapters go beyond what is traditionally covered in an introductory course. The goal of the presentation is to provide the students with a solid background in quantum mechanics.Mathematical Preliminaries
Free-Particle Schrödinger Equation: Wave Packets
Schrödinger’s Equation with Potential Energy: Introduction to Operators
Postulates and Basic Elements of Quantum Mechanics: Properties of Operators
Problems in One-Dimension: General Considerations, Infinite Well Potential, Piecewise Constant Potentials, and Delta Function Potentials
Simple Harmonic Oscillator: One Dimension
Problems in Two and Three-Dimensions: General Considerations
Central Forces and Angular Momentum
Spherically Symmetric Potentials: Radial Equation
Dirac Notation
Spin
(A) Review of Basic Concepts (B) Feynman Path Integral Approach (C) Bell’s Inequalities Revisited
Perturbation Theory
Variational Approach
WKB Approximation
Scattering: 1-D
Scattering: 3-D
Symmetry and Transformations: Rotation Matrices
Addition of Angular Momenta, Clebsch-Gordan Coefficients, Vector and Tensor Operators, Wigner-Eckart Theorem
Hydrogen Atom with Spin in External Fields
Time-Dependent Problems
Approximation Techniques in Time-Dependent Problems
Decay of a Discrete State into a Continuum of States: Fermi’s Golden Rule