Nonrelativistic Quantum Mechanics
Book Description
This book is now out of print and is superceded by the third edition.
Reviews:
In a foreword, the editor mentions as his criteria for selection of manuscripts: "clarity and soundness of treatment ... as well as the freshness of the approach." A better choice could not indeed have been made to reach these goals than this textbook by Capri. His presentation of nonrelativistic quantum mechanics is that of a mathematically sound theory; his book does much for this theory to be recognized as the inherently elegant and simple one that it is. The author shows much respect for his readers by striving not to let any conceptual or calculational difficulty slip by unnoticed. He is careful in his selection of examples, showing a great desire for clarity as well as for relevance to contemporary applications. His choice of material, some of which is not normally found in textbooks at this level, is such as to provide the student with an excellent preparation for further studies in any modern branch of more advanced quantum mechanics.
Gilles Labonté,Royal Military College of Canada, Foundations of Physics, 1987.
Non-relativistic quantum mechanics as commonly practised has been bad for the mathematical hygiene of physics as a whole: almost as bad as thermodynamics, though it has not yet drawn such devastating broadsides as Truesdell has delivered against the traditional textbook versions of the latter. The structure, say as it left the hands of Dirac, is so robust that enormous amounts of marvellous physics can be elicited from it by mathematics so shoddy as to offend not just against some fanciful notions of rigour, but against the most elementary canons of selfconsistency and common sense. (Anyone inclined to doubt this should consider, for example, some textbook discussions touching both on infinitely-high potential steps and on the momentum operator.) Of course the blame is shared by the mathematicians, for believing far too persistently that the theoretical constructs used by the physicists were not respectable, merely because mathematics had been so slow in defining them to its own satisfaction (witness for instance the book by von Neumann and the history of the delta function).
Nevertheless, in the long run it is perilous for physics that non-relativistic quantum mechanics (or indeed any other part of it) should be introduced in ways calculated to make any moderately critical student doubt either his own reason or his teacher's. The relatively simple mathematical ideas for relieving such conceptual strains have been available for some time, however, they confer few if any computational perks, and they have made next to no impact on undergraduate physics teaching, nor probably on most postgraduate physics courses.
The overriding merit of Capri's book is that he exploits the requisite mathematics, without fuss, at a level appropriate to an introductory course, taking great pains to explain its relevance to the physics. As far as the reviewer can tell this is the first such attempt in any text intended, like Capri's, as a thorough introduction at the undergraduate level, extending perhaps to first-year graduate work. The physics community is much in his debt and one must hope that in this respect his fashion will be followed by future textbook writers. It is especially impressive that these path-breaking sections, sensibly introducing the notions of functionals, selfadjoint operators, selfadjoint extensions, and rigged Hilbert spaces, occur relatively early, instead of being relegated apologetically to the end of the book, as by many of us they might have been.
The bulk of the book necessarily deals with matters that are quite standard. In this area the reviewer believes that even if not all possible good books have yet been written, all but a very few such chapters have, at least for the present generation. Consequently, chapter by chapter the only relevant comparison is with the very best, and here readers' reactions might vary. As regards presentation, there are especially pleasing sections on the correspondence principle applied to hydrogen; on the mathematical facts underlying the single-valuedness of orbital wavefunctions (albeit without proofs); on time delays in scattering, and on second quantization and the symmetry properties of wavefunctions for identical particles. On the other hand, the reviewer suspects that much of the discussion of scattering theory, say, is not pitched in the manner most likely to smooth the path of the first-time leamer, and (as in several other books) the Born approximation to the hydrogen photoeffect is introduced in the classic manner that eventually misapproximates the matrix element by a factor of two.
As regards selection, it is a measure of the admiration aroused by the author in other respects that in more routine matters some of his omissions should seem so disappointing, though most such complaints arc bound to be rather subjective. For instance, on two-level systems one misses the rotating-wave approximation and the Rabi equations; the diamagnetic term in the current operator appears occasionally to slip out of sight gauge-invariance is curiously underplayed; the Bohm-Aharanov effect is not dealt with; and Bell inequality rates a bare mention at the very end. However, if there is any justice, the book is destined for a long and distinguished career, and successive editions will no doubt allow such details to mature. As it stands, the book is already a must for teachers, and selected chapters from it a godsend for intelligent and self-respecting students.
The pages are reproduced from camera-ready typescript, and the equations are reasonably easy to read. There are relatively few misprints.
Dr G. Barton, University of Sussex, Contemporary Physics Vol 29 #1, Jan/Feb 1987.
Anton Capri's book is an extensive and modern treatment of nonrelativistic quantum mechanics suitable for a two-semester undergraduate or one-semester graduate course. Essentially all of the standard topics are covered, although with an unstated bias towards the physics of nuclei and elementary particles as compared with condensed matter physics.
The author makes a noteworthy attempt to introduce more mathematical detail than is usual in his discussion of the linear space structure of quantum mechanics. The ideas of Schwartz spaces, dual spaces and rigged Hilbert spaces, and the distinction between strong and weak convergence, are clearly introduced, and the treatment of standard problems and techniques is uniformly good. I was pleased by the discussion of the WKB method and of the Glauber approximation for scattering theory. Capri is aware of the quantum Hall effect, and includes a nice account of the effect of a magnetic field and gauge invariance upon electron motion. He concludes with an introduction to second quantization and a brief description of density matrix methods. This book should be carefully considered for use in advanced undergraduate or early graduate courses.
R.B. Jones, Nature, 1987.