A Concise Introduction to Quantum Mechanics / Edition 1

by Mark S Swanson

Overview

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 analyze the system consisting of a particle confined 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. The general properties of the Schrödinger equation and its solutions are analyzed, and the theory of observables is developed along with the associated Heisenberg uncertainty principle. Basic applications of wave mechanics are made to free wave packet spreading, barrier penetration, the simple harmonic oscillator, the Hydrogen atom, and an electric charge in a uniform magnetic field. In addition, Dirac notation, elements of Hilbert space theory, operator techniques, and matrix algebra are presented and used to analyze coherent states, the linear potential, two state oscillations, and electron diffraction. 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.

Product Details

ISBN-13:	9781681747170
Publisher:	Morgan and Claypool Publishers
Publication date:	05/10/2018
Series:	Iop Concise Physics
Pages:	183
Product dimensions:	7.00(w) x 10.00(h) x 0.00(d)

About the Author

Mark 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

Table of Contents: Preface / Author biography / 1. Classical mechanics and electromagnetism / 2. The origins of quantum mechanics / 3. The wave function / 4. Wave mechanics / 5. Applications of wave mechanics / 6. Dirac notation, operators, and matrices / 7. Angular momentum, spin, and statistics / 8. Bibliography