Nonrelativistic Quantum Mechanics, Third Edition
Book Description
Reviews:
I shall review this extremely valuable pair of books together, as they are closely related, referring to the textbook Nonrelativistic Quantum Mechanics as ‘NQM’ and the accompanying volume Problems and Solutions in Nonrelativistic Quantum Mechanics as ‘P&S’. There has been a great proliferation of quantum mechanics texts in the last few years at all levels of sophistication, so new entries to this crowded market (or in the case of NQM, a new edition of an existing text) need something distinctive to recommend them. In the preface to NQM Capri tells us that he has taught quantum mechanics at several different levels, but the result of his labours is a text that reads very much like a graduate textbook for the North market such as Jackson's Classical Electrodynamics or Goldstein's Classical Mechanics. NQM shares some of the qualities of these texts: the exposition starts from the fundamentals but proceeds fairly rapidly to quite difficult material. and gives a detailed and balanced account of the whole subject. This makes it unsuitable for most British undergraduates as an introductory text, but accessible to students studying at a slightly more advanced level, and of great value to the professional as giving authoritative and detailed treatments of tricky points that are glossed over in more introductory texts. Indeed, anyone teaching quantum mechanics would benefit from owning both books..
The opening chapters relate how quantum mechanics emerged from the breakdown of classical physics, in a broadlv historical development. In particular Chapter 2 describes analytical mechanics in sufficient detail to explain how Bohr-Sommerfeld quantization worked in old quantum theory. This chapter is far too dense, consisting essentially of the whole of Goldstein’s text condensed into about sixteen pages, but it is a brave attempt to cover a lot of interesting ground before getting started on the ‘new’ quantum mechanics, and it enables quite a lot of connections to be made between quantum and classical results in the remainder of the book. The next few chapters cover the usual topics concentrating on solvable problems like the particle in a box the harmonic oscillator and central potentials. Two topics in this section call for particular mention. First, chapters 6 and 8 contain much more careful, while still accessible discussion of operators and their properties and distribution theory and rigged Hilbert space than is customary outside quite dense monographs and this is one of the distinctive features which picks out this text from the competition. Second, Chapter 7 discusses all aspects of the physical interpreta tion in one coherent exposition which has the great merit of making the rough edges of the standard interpretation rather obvious. The solvable problems are naturally followed by perturbation theory, the treatment of which is excellent with standard Rayleigh-Schrödinger theory treated in considerable detail followed by a parallel discussion of it together with Brillouin -Wigner theory The final chapters look at scattering theory and many particle systems.
The adjective ‘nonrelativistic’ in the title gives coherence to the material as there is a careful exclusion of any relativistic corrections. Thus, in the scattering section only nonrelativistic kinematics is considered while the earlier discussion of the hydrogen atom omits all the order α2 terms. This limiting of scope enables real clarity in the exposition particularly in the comparisons with classical mechanics.
My criticisms of the text are comparatively minor by comparison and I shall mention only one. The preface tells us that the author is a fairly recent convert to the use of TEX which suggests although the title page does not confirm this that we arc looking directly at the authors typesetting in TEX . The book design has some of the defects identified by Lamport in LaTeX: a Document Preparation System as typical of work prepared in this way: cross-references are badly handled and the layout of material such as definitions and theorems appears to be handled on a case-by-case basis. Some late reordering of material is apparent in Chapter 11 where there is a sudden rash of typographical errors and a backward reference (as we have seen) to a topic not introduced until several pages later.
Turning more briefly to the companion volume P&S it consists of a large collection of solved problems with the same set of chapter titles as NQM. However the relation ship between the two books is not straightforward: some of the problems in NQM are not solved in P&S while some of the problems in P&S are not set in NQM. Some of the new material in P&S serves to highlight omissions in the textbook: for example Chapter 7 contains some very interesting problems on the Wigner function which is entirely omitted from NQM. This problem set is an extremely valuable resource. The two volumes together contain a huge quantity of material much of it slightly unusual or treated in more detail than is often the case and they should be available to anyone whose work involves the use of quantum mechanics.
C. W. P. Palmer(University of Oxford), Contemporary Physics, 2004
This is an introduction to quantum mechanics for those who want to be honest. The standard topics are covered, but the particular virtue is that many of the places where one fibs to the students are here covered with enough attention to the mathematics to make sense. Why is there no self-adjoint time operator? Why can radial momentum not be made self adjoint? Why must angular momentum eigenfunctions be single valued? What is the physical significance of deficiency indices? (Few authors have the courage to take up the last topic, and yet its physical implications are significant.) Capri manages to cover these issues with explanations comprehensible to undergraduates who have not studied functional analysis. The book of problems is a helpful complement and can be used profitably by an instructor both to suit individual tastes and to provide deeper coverage of particular topics. In its third edition, this set of books will continue to provide an excellent foundation for this most important course in the preparation of a physicist.
L. S. Schulman
"Nonrelativistic Quantum Mechanics", by Anton Z. Capri is an excellent and delightful textbook for students and teachers of advanced undergraduate and graduate courses. Its lucid style makes it ideal for self study. The instructive problems and the bibliography emphasizing original references at the end of each chapter make it valuable for the student and teacher alike.
The first four chapters dealing with historical origins, elementary systems and one dimensional systems of quantum mechanics build up the understanding and basic skills of the student. The author's mastery of the subject and teaching skills show through in the superb sections on mathematical foundations (especially self-adjoint operators) and Distributions and Fourier Transforms (especially Rigged hilbert spaces). They instill confidence and show the direction towards rigour in dealing with eigenfunction expansions, time-energy uncertainty relations, Dirac Delta funtions and unnormalizable momentum 'eigen functions' without getting involved in heavy mathematics. Algebraic methods, central force problems, transformation theory, stationary and time-dependent perturbation theory, Rayleigh-Ritz variational principle, WKB approximation, scattering theory, particles in electromagnetic fields, atomic spectra, identical particles, second quantization and quantum statistical mechanics are some of the topics beautifully explained with numerous practical illustrations and problems. Special mention may be made of the modern topics of coherent states, squeezed states, tunneling, Berry's phase, quantum Hall effect , Aharonov-Bohm effect and density matrices in quantum statistical mechanics which make thebook very useful and up to date.
In summary, it is a comprehensive book touching nearly all aspects of non-relativistic quantum mechanics. It makes learning a pleasure due tothe elegant effortless style.
Shasanka Mohan Roy, Tata Institute of Fundamental Research