Topics in quantum mechanics
type: Item
instance of: scholarly article
title: Topics in quantum mechanics
zbMATH Open document ID: 1026.81001
author: Floyd L. Williams
published in: Progress in Mathematical Physics
publication date: 2003-05-08T00:00:00Z
review text: The book consists of two parts that are rather different in character. The first part is about the basics of quantum mechanics with very detailed calculations. Contrary to the usual habit setting the physical constants in a suitable way to one they are kept all the time. The second part focuses on path integrals and zeta functions and discusses their use in quantum statistical mechanics. The last chapter, contributed by P. Shanahan, gives a short introduction to gauge theory. Chapter 0 introduces the basic physical quantities like length, mass, force, energy etc. as well as their units. The last point is certainly interesting for mathematicians who in most cases ignore physical constants and their units. The units are given in the cgs system. The SI system is mentioned only at the end of the chapter. In Chapter 1 some of the ideas at the beginning of the 20th century which led to quantum mechanics are reviewed. Starting with some remarks on Planck's quantization this chapter presents Bohr's frequency rules and the emission spectra for the hydrogen atom. Then Schrödinger's equation is introduced, followed by a discussion of the de Broglie wavelength and Heisenberg's uncertainty principle where the slit experiment is considered. Finally the particle-wave dualism is noted in the section about Bohr's complementary principle. The next chapter introduces elementarily some concepts of classical mechanics. It begins with Newton's law for the equation of motion to proceed with the explicit calculation of some examples in one dimension. After passing to three dimensions Hamilton's and Lagrange's equations of motion are introduced and again some examples like a ball in constant gravitational field are calculated in detail. This chapter also deals with many particle problems and the transformation into centre of mass coordinates is presented. Chapter 3 deals with the Schrödinger equation, first written in the time dependent way \(i\hbar {\partial \psi \over \partial t} = {\part…
reviewed by: Eckhard Giere
Mathematics Subject Classification ID: 81-01
Mathematics Subject Classification ID: 35J10
Mathematics Subject Classification ID: 81T13
Mathematics Subject Classification ID: 81Q05
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 81V45
Mathematics Subject Classification ID: 81Q15
Mathematics Subject Classification ID: 20C30
Mathematics Subject Classification ID: 81Q30
Mathematics Subject Classification ID: 81R05
Mathematics Subject Classification ID: 81T20
Mathematics Subject Classification ID: 70H03
Mathematics Subject Classification ID: 70H05
zbMATH DE Number: 1907573
zbMATH Keywords: quantum mechanics
zbMATH Keywords: hydrogen atom
zbMATH Keywords: harmonic oscillator
zbMATH Keywords: hypergeometric functions
zbMATH Keywords: selection rules
zbMATH Keywords: zeta function
zbMATH Keywords: quantum statistical mechanics
zbMATH Keywords: representation of groups
zbMATH Keywords: gauge theory
zbMATH Keywords: Feynman path integrals
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1907573