A Concise Introduction to Quantum Mechanics
- Mark S Swanson
- February 2018
Assuming a background in basic classical physics, multivariable calculus, and diﬀerential equations, A Concise Introduction to Quantum Mechanics provides a self-contained presentation of the mathematics and physics of quantum mechanics. The relevant aspects of classical mechanics and electrodynamics are reviewed, and the basic concepts of wave-particle duality are developed as a logical outgrowth of experiments involving blackbody radiation, the photoelectric eﬀect, and electron diﬀraction. The Copenhagen interpretation of the wave function and its relation to the particle probability density is presented in conjunction with Fourier analysis and its generalization to function spaces. These concepts are combined to analyse the system consisting of a particle conﬁned to a box, developing the probabilistic interpretation of observations and their associated expectation values. The Schrödinger equation is then derived by using these results and demanding both Galilean invariance of the probability density and Newtonian energy-momentum relations. In addition, Dirac notation, elements of Hilbert space theory, operator techniques, and matrix algebra are presented. Applications are made to photon and electron spin and the addition of angular momentum, and direct product multiparticle states are used to formulate both the Pauli exclusion principle and quantum decoherence. The book concludes with an introduction to the rotation group and the general properties of angular momentum.
About EditorsMark Swanson, PhD, is Emeritus Professor of Physics at the University of Connecticut and lives in Monroe, Connecticut. He received his PhD in physics from the University of Missouri at Columbia. He held postdoctoral appointments at the University of Alberta and the University of Connecticut, as well as a faculty appointment at the University of Connecticut at Stamford. He is the author of 25 research articles and two monographs, with an emphasis on ﬁeld theory and path integral techniques.
Table of Contents
Paperback ISBN: 9780750329026
Ebook ISBN: 9781681747194
Publisher: Morgan & Claypool Publishers