Introductory Quantum Mechanics

Paul R. Berman is a Physics Professor at the University of Michigan. He is a Fellow of the American Physical Society and the Optical Society of America. Among topics he is currently investigating are microscopic theories of atom-field interactions in dielectrics, spin squeezing, storing quantum information, light scattering, collective emission, and pedagogical problems in atom-field interactions.

“The book is based on junior and senior level undergraduate courses … . the author discusses some open conceptual problems of quantum physics and his own position with respect to them. This makes the exposition more modern and vivid. … Almost each chapter is enriched with appendices with more advanced material.” (Yana Kinderknecht, zbMATH 1394.81001, 2018)

• Introduction.- Mathematical Introduction.- Free Particle Schroedinger Equation - Free-Particle Wave Packets.- Schroedinger's Equation with Potential Energy: Introduction to Operators.- Postulates and Basic Elements of Quantum Mechanics: Properties of Operators.- Problems in 1-dimension: General Considerations, Infinite Well Potential, Piecewise Constant Potentials, and Delta Function Potentials.- Simple Harmonic Oscillator - One Dimension.- Problems in 2 and 3-dimensions - General Considerations.- Central Forces and Angular Momentum.- Spherically Symmetric Potentials - Radial Equation.- Dirac Notation.- Spin.- Important Basics from Phys 453.- Perturbation Theory.- Variational Approach.- WKB Approximation.- Scattering - 1-D.- Scattering - 3-D.- Symmetries and Transformations.- Rotations - Examples.- Addition of Angular Momentum: Clebsch-Gordan Coefficients.- Vector and Tensor Operators: Wigner-Eckart Theorem.- Spin-Orbit Interactions - Hydrogen Atom with Spin in External Fields.- Time-Dependent Problems.- Approximation Techniques in Time-Dependent Problems.- Fermi's Golden Rule.