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. Alkofer, E. Frey, and H.-T. Janka. Careful reading of the proofs by Chr. Baumgiirlel, R. Eckl, N. Knoblauch, J. Krumrey, w. Rossmann-Bloeck and M. Zobel 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, to Mrs. H. Sprzagalla for typing the original manuscript, and to all my other colleagues who gave important assistance in producing this book, as well as to the publisher.

Fast Orientation Mapping from HARDI

“…1) can be expressed in spherical coordinates. This is a consequence of the pointwise convergent expansion of the plane wave in spherical coordinates [12] given by …”

On transition rates in surface hopping

“…Note that in (3) we neglected the terms φ i (r; R)|T |φ j (r; R) , being of order 1/M smaller than the kinetic energy of the electrons. 19 The NAC vectors D ij (R) couple different adiabatic energy surfaces. Generally, the coupling terms in Eq.…”

“…Generally, the coupling terms in Eq. (3) are of order 1/ √ M smaller than the electronic energy, 19 and therefore they can be safely neglected. In this case, the adiabatic nuclear wave functions are evolved independently, i.e., their normalizations-which give the adiabatic populations-are constants of motion.…”

“…In this case, Eq. (19) indicates that the direction of D 12 is along E and μ is proportional to the tensor product E ⊗ E . This further supports ansatz (12), witĥ μ ∝ D 0 ⊗ D 0 , for the NACs, and our findings of Sec.…”

Supersymmetry and the Hartmann potential of theoretical chemistry

“…The challenge then in using SUSYQM techniques is not in the mechanics of the construction of just any SUSY hamiltonian, but in finding a suitable superpotential (or V 1 (x)) to construct a SUSY hamiltonian which will be relevant to the problem at hand. It is a common practice to choose or pose as an ansatz the W 1 to solve a physical problem [11,12].…”