Topics in Quantum Mechanics

ISBN-13: 9781461265719 / Angielski / Miękka / 2012 / 398 str.

Floyd Williams

Opis

This self-contained text presents quantum mechanics from the point of view of some computational examples with a mixture of mathematical clarity often not found in texts offering only a purely physical point of view. Emphasis is placed on the systematic application of the Nikiforov-- Uvarov theory of generalized hypergeometric differential equations to solve the Schr"dinger equation and to obtain the quantization of energies from a single unified point of view.

Recenzje

". . . 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

Spis treści

Preface * Part I. Introductory Concepts in Quantum Theory * Units of Measurement * Quantum Mechanics---Some Remarks and Themes * Equations of Motion in Classical Mechanics * Quantization and the Schrödinger Equation * Hypergeometric Equations and Special Functions * Hydrogen-like Atoms * Heisenberg's Uncertainty Principle * Group Representations and Selection Rules * A Charged Particle in an Electro-magnetic Field * Spin Wave Functions * Introduction to Multi-electron Atoms * Part II. Some Selected Topics * Fresnel Integrals and Feynman Integrals * Path Integral for the Harmonic Oscillator * Euclidean Path Integrals * The Density Matrix and Partition Function * Zeta Regularization * Helmholtz Free Energy and the Selberg Trace Formula * The Zeta Function of a Product * Two Guest Lectures * Some Further Electron Configurations * Mendeléev Periodic Table * Another Example of Zeta Regularization * Integral Evaluation * Some Informal Comments on QFT * References * Index

O autorze

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.