Levinson, I B

Vanagas, V V

Yutsis, A P

English

IACS Institutional Repository

BOOK REVIEWMATHEMATICAL APPARATUS OF THE THEORY OF ANGULAR MOMEN­TUM—by A. P. Yutsis, I. B. Levinson and V. V. Vanagas. Published by the Israel Program for Scientific translation. Price...The book under review, an English translation from the original Russian, is an important and fruitful contribution to the current literature on the highly useful and specialized branch of quantum mechanics—the theory of angular momentum. It starts with a brief discussion of tlio relation between angular momentum operators and spatial rotations. The subsequent chapters mainly deal to begin with the problem of vector addition of two angular momenta, then with the problem of addition of an arbitrary number of angular momenta, and finally discuss the various properties of vector coupling co-eflScients. A major part has been devoted to the highly useful graphical methods for operations with Jm - and 3'/i/*eoefficients, and properties of irreducible t(msor operators and their matric elements. The book thus, may bo considered as a review of the properties of vector coupling co-cfficionts — the so-called CIcbs-Gordon and Wigner coeffi­cients, an important mathematical apparatus in the quantum mecdianical calcula­tions involving the coupling of a number of angular momentum operators. In vector coupling problem, one usually finds various terminologies, used by different workers such as Clebs-Gordon coefficients, Wigner coefficients, Racah’s If-coeffi- cients, 3 -coefficients, Jm-coefficionts, 3w.J-coofficients etc., between which con­fusion in definitions is often met with in literature. The authors have, carefully and preserved their distinction to their as well as readers' convenience with specific definition for each of them.The authors appear to have assumed the reader’s preliminary acquaintance with the methods of group theory and the properties of quantum mechanical angular momentum operator and one encounters the frequent reference to Condon and Shortby’s book “The Theory of Atomic Spectra”, Wigner’s book “Group theory” and Racah’s work (1042, Rhys. Rev). Moreover, many of the results and mathe­matical inferences have been simply quoted without giving their proofs, perhaps to avoid cumbrous and tedious algebraic computation. Stress has been laid on the methods of calculation rather than on the derivation of those methods. Of course, the authors did not fail to give the complete references of the original works where an inquisitive reader may find the necessary proofs to his satisfaction. On the whole, the book will be highly useful to the scientific workers engaged in advanced research in many branches of Theoretical Physics, and interested more in having the ready formulae and methods of calculation rather than in their complicated derivations.602Booh Review 6 0 3As stated earlier, the present contribution is a translation from the original Russian and the reviewer is unable to assure the faithfullness to the translations. However, the translator in his note admits that ‘ t^ranslation, unlike rotation, cannot be always represented in a ‘unitary’ form” . Even assuming unavoidable devia­tions from the original Russian, the translation lacks no clarity, continuity and lucidity of exposition,U, S, Ohosh

Mathematical Apparatus of the Theory of Angular Momentum

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Mathematical Apparatus of the Theory of Angular Momentum

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