Topics in Quantum Mechanics

An exciting monograph of some new applications of so-called pure mathematics, including number theory, to various problems arising in quantum field theory. A self-contained unique treatment using conventional math terminology. Introductory material on Planck, Schr"dinger quantization, Pauli's spin functions, multielectron atoms; more advanced topics include: Feynman path integrals, quantum partition functions, zeta functions, spherical harmonic analysis and the Selberg trace formula. Good bibliography and index. An excellent resource for clasroom or self-study.

". . . a number of interesting and classical applications (some involving detailed computations) are included. Most of the book is dedicated to covering the traditional material but there are also some innovations, both in the choice of topics and in the way they are presented. . . . overall, I shall say that this is a very good text that is welcome both from the conceptual and the operational points of view. The theoretical physics community should also find here a good source on the subject."

Mathematical Reviews

Autorentext
An exciting monograph of some new applications of so-called pure
mathematics, including number theory, to various problems arising in
quantum field theory. A self-contained unique treatment using
conventional math terminology. Introductory material on Planck,
Schr"dinger quantization, Pauli's spin functions, multielectron atoms;
more advanced topics include: Feynman path integrals, quantum
partition functions, zeta functions, spherical harmonic analysis and
the Selberg trace formula. Good bibliography and index. An excellent
resource for clasroom or self-study.

Inhalt
I Introductory Concepts in Quantum Theory.- 0 Units of Measurement.- 1 Quantum Mechanics: Some Remarks and Themes.- 2 Equations of Motion in Classical Mechanics.- 3 Quantization and the Schrödinger Equation.- 4 Hypergeometric Equations and Special Functions.- 5 Hydrogen-like Atoms.- 6 Heisenberg's Uncertainty Principle.- 7 Group Representations and Selection Rules.- 8 The Quantized Hamiltonian for a Charged Particle in an Electromagnetic Field.- 9 Spin Wave Functions.- 10 Introduction to Multi-Electron Atoms.- II Some Selected Topics.- 11 Fresnel Integrals and Feynman Integrals.- 12 Path Integral for the Harmonic Oscillator.- 13 Euclidean Path Integrals.- 14 The Density Matrix and Partition Function in Quantum Statistical Mechanics.- 15 Zeta Regularization.- 16 Helmholtz Free Energy for Certain Negatively Curved Space-Times, and the Selberg Trace Formula.- 17 The Zeta Function of a Product of Laplace Operators and the Multiplicative Anomaly for X?d.- 18 Schrödinger's Equation and Gauge Theory.- About the Author.- General Appendices.- Appendix A: Some Further Electron Configurations.- Appendix B: Mendeléev Periodic Table.- Appendix C: Determinants for String World-Sheets That Are Tori: Another Example of Zeta Regularization.- Appendix E: Some Informal Comments on QFT.- References.