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Physics Bulletin

The Quantum Mechanical Three Body Problem

G. Barton

Published Apr 1, 1975• 14 citations
Publisher

Abstract

Erich W Schmid and Horst Ziegelmann Braunschweig: F Vieweg 1974 pp vi + 218 price DM 58 Up till now, neither textbooks nor monographs on quantum mechanics or scattering theory have, on the whole, given proper weight to the fact that in quantum mechanics the three body problem has been solved. Since its solution is a major achievement of mathematical physics, such omissions were regrettable and increasingly hard to defend.

DOI
10.1088/0031-9112/26/4/030

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Erich W Schmid and Horst Ziegelmann Braunschweig: F Vieweg 1974 pp vi + 218 price DM 58 Up till now, neither textbooks nor monographs on quantum mechanics or scattering theory have, on the whole, given proper weight to the fact that in quantum mechanics the three body problem has been solved. Since its solution is a major achievement of mathematical physics, such omissions were regrettable and increasingly hard to defend.
F Constantinescu and E Magyari Oxford: Pergamon 1971 pp vii + 410 price £5.70 This is a translation of a book apparently first published in eastern Europe two or three years ago and aimed at advanced undergraduates and beginning research students. It contains 319 solved problems, arranged in a dozen subject groups which include not only reasonably high level treatments of the standard topics (mathematical formalism, onedimensional models, angular momentum, atoms and molecules, various approximation methods) but also large sections on systems of identical particles and second quantization, on scattering theory and on relativistic quantum mechanics (the last two subjects together occupying over a quarter of the book).
By I. I. Goldman, V. D. Krivchenkov, V. I. Kogan and V. M. Galitskii. Translated, edited and arranged by D. ter Haar. London : Cleaver-Hume Press Ltd. Pp. 394. Price 42s. It has always been accepted that one cannot learn mathematics without solving a large number of problems, and the same is true of mathematical physics. Unfortunately the problems in many books on quantum mechanics are either purely mathematical or else present extensions of the subject matter of the book, which space has prevented from incorporation in the text.
This book contains more than 300 problems in quantum mechanics with accompanying solutions, covering topics that are commonly taught in first-year graduate physics programs. Special care is given to each problem's formulation, with detailed and extensive solutions provided to support understanding. The problems span a range of difficulties, from basic exercises to more challenging applications and extensions of the standard material. Students are required to think critically and incorporate physics and mathematical techniques learned previously or concurrently to solve the more challenging problems. Each chapter begins by framing the particular topic being examined with a short theory section that sets the context for and motivates the problems that follow. This text is well suited for self-study or as a useful supplement to the existing quantum mechanics textbooks for upper-undergraduate and graduate students, and their instructors.