Physics of many-particle systems : methods and problems

Paul C. Martin, Julian Schwinger

Viktor Mikhaĭlovich Galit︠s︡kiĭ, Boris Mikhailovich Karnakov, Vladimir I Kogan

The book contains 800 problems mainly on non-relativistic quantum mechanics, covering both the basic provisions and mathematical apparatus of the theory, as well as its numerous applications to atomic physics, nuclear and particle physics and physics of multiparticle systems. Considerable attention is paid to the computational methods of quantum mechanics: perturbation theory, quasiclassical approximation, variational method, sudden impact approximation, adiabatic method. Two chapters (out of a total of 16) include problems on elementary quantum radiation theory and relativistic wave equations. These problems are a useful introduction to the study of quantum field theory and particle physics.

N.P. Klepikov

An active transformation of a physical system implies its motion. A passive transformation of the system is a change in the method of describing it. An analogy transformation means transition to another physical system, similar in some respect to the original one. In some cases transformations of one type may imitate those of another. The operation of particle permutation in quantum mechanics implies a passive transition to describing the same state of the system by a different method of introducing particle numbering. The problems of transitions from describing identical particles to describing different ones and that of explaining the probabilistic meaning of wave functions statistically are touched upon.

Eberhard Zeidler

Michael Danos, Vincent P. Gillet

This book is concerned with the practical aspects of solving angular momentum problems. The novel but fully tested-out method (the Invariant Graph Method) allows one to write down from a single graph the complete final result of the problem. The drawing of the graph involves very few simple, essentially self-evident rules. Still it is a powerful tool to easily solve the most involved physical problems. The method is introduced step-by-step in a sequence of examples, beginning with the simplest matrix elements, and ending with the most general case of a reaction including angular distributions and correlations. The many-body and particle anti-particle systems are fully developed. All aspects: wave functions, vectors, operators, Fock space state vectors and operators, etc., are treated on the same footing. All concepts of angular momentum theory acquire a transparent meaning. Hence the book is valuable not only as a handbook in problem solving, but extremely so as an adjunct in any course on advanced qunatum physics, atomic, molecular, nuclear and particle physics