Quantum Mechanics

Abstract

This is a textbook on quantum mechanics. In an introductory chapter, the basic postulates are established, beginning with the historical development, by the analysis of an interference experiment. From then on the organization is purely deductive. In addition to the basic ideas and numerous applications, new aspects of quantum mechanics and their experimental tests are presented. In the text, emphasis is placed on a concise, yet self-contained, presentation. The comprehensibility is guaranteed by giving all mathematical steps and by carrying out the intermediate calculations completely and thoroughly.The book treats nonrelativistic quantum mechanics without second quantization, except for an elementary treatment of the quantization of the radiation field in the context of optical transitions. Aside from the essential core of quantum mechanics, within which scattering theory, time-dependent phenomena, and the density matrix are thoroughly discussed, the book presents the theory of measurement and the Bell inequality. The penultimate chapter is devoted to supersymmetric quantum mechanics, a topic which to date has only been accessible in the research literature.For didactic reasons, we begin with wave mechanics; from Chap. 8 on we introduce the Dirac notation. Intermediate calculations and remarks not essential for comprehension are presented in small print. Only in the somewhat more advanced sections are references given, which even there, are not intended to be complete, but rather to stimulate further reading. Problems at the end of the chapters are intended to consolidate the student's knowledge.The book is recommended to students of physics and related areas with some knowledge of mechanics and classical electrodynamics, and we hope it will augment teaching material already available.This book came about as the result of lectures on quantum mechanics given by the author since 1973 at the University of Linz and the Technical University of Munich. Some parts of the original rough draft, figures, and tables were completed with the help of R. Alkover, E. Frey and H.-T. Janka. Careful reading of the proofs by Chr. Baumgartel, R. Eckl, N. Knoblauch, J. Krumrey and W. Rossmann-Bloeck ensured the factual accuracy of the translation. W. Gasser read the entire manuscript and made useful suggestions about many of the chapters of the book. Here, I would like to express my sincere gratitude to them, and to all my other colleagues who gave important assistance in producing this book, as well as to the publisher.

Proposal to improve the behaviour of self-energy contributions to the S-matrix

“…In the first example we found that our formalism reproduces the results that can be obtained by RayleighSchrödinger perturbation theory (see e.g. [17]) and gives the result that the S-matrix is the identity operator, in accordance with the remarks in 4. in Sec. 2.3.…”

“…The right hand sides of (10) and (11) written in the above form (17), (18) are very similar to the formula introduced by Gell-Mann and Low in [5] (see also [6]), which serves to produce the vacuum state of H from the vacuum state of H 0 .…”

“…This is true for our formulas (17) and (18) as well, since the factors X (−T ) and X (T ) are real. Let us introduce | (−T ) and | (T ) as…”

Colored scalar in a chromomagnetic field

“…(8) is universal for color index ( ), any of these states may have any energy from the spectra (9) or (12). This quantization is similar to one for the momentum in standing waves [17]. The wave function (11) on the ( ) plane gives us a distribution picture, which consist of rings of maxima and minima corresponding to the maxima and zeros of the Bessel function.…”

Thermalization of Nonequilibrium Electrons in Quantum Wires

“…which can be solved with help of an operator-algebra technique known from the harmonic oscillator problem [17]. The eigenvalue problem in Eq.…”