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Physics Bulletin

Mathematics and wave Mechanics

Leslie Howarth

Published Jul 1, 1957• 2 citations
Publisher

Abstract

By R. H. Atkin London : William Heinemann Ltd. Pp. 348 + xv. Price 30s. This is a difficult book for a professional mathematician to review since it's neither aimed at him nor primarily at his students. In his preface the author says that: "Assuming the reader's mathematics is reliable at a level which he would normally reach prior to entering a University, I have tried to select a course of study which is logically connected and yet adequate for the pursuit of modern quantum theory....

DOI
10.1088/0031-9112/8/7/007

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By R. H. Atkin London : William Heinemann Ltd. Pp. 348 + xv. Price 30s. This is a difficult book for a professional mathematician to review since it's neither aimed at him nor primarily at his students. In his preface the author says that: "Assuming the reader's mathematics is reliable at a level which he would normally reach prior to entering a University, I have tried to select a course of study which is logically connected and yet adequate for the pursuit of modern quantum theory....
Quantum mechanics is one of the principle pillars of modern physics. It also remains a topic of great interest to mathematicians. Since its discovery it has inspired and been inspired by many topics within modern mathematics, including functional analysis and operator algebras, Lie groups, Lie algebras and their representations, principle bundles, distribution theory, and much more. Written with beginning graduate students in mathematics in mind, this book provides a thorough treatment of (nonrelativistic) quantum mechanics in a style that is leisurely, without the usual theorem-proof grammar of pure mathematics, while remaining mathematically honest. The author takes the time to fully develop the required mathematics and employs a consistent mathematical presentation to clarify the often-confusing notation of physics texts. Along the way the reader encounters several topics requiring more advanced mathematics than found in many discussions of the subject, making for a fascinating course in how mathematics and physics interact.
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.
Abstract This book provides the reader with a contemporary and comprehensive introduction to Quantum Mechanics. It is suitable for beginners as well as for more advanced university students. Quantum mechanics is presented in a pedagogical fashion, with a clear logical organization. The various concepts and methods are introduced first in elementary terms, and later developed into more precise formulations. Systematic studies of approximation methods and the discussion of a wide class of physical applications follow. Part I of the book, together with the opening sections of Part II, provide adequate material for an introductory course of one semester at most universities. The rest of the book might be used in an advanced course on Quantum Mechanics. The basic material is fairly standard, even though some discussions such as those on general systems with time-dependent Hamiltonians, on metastable systems, as well as the discussions in some of the Complement sections, may not be found in other textbooks. The book also contains many original observations or new ways of illustrating even well-known subjects. In fact, the authors wish to convey in this book the sense of wonder in the logical simplicity and at the same time the beauty of subtle and far-reaching consequences of Quantum Mechanics, to young physics students in particular. Problem sets are provided at the end of each chapter, to be solved either analytically or by numerical methods. The solutions to both types of problems are given as separate pdf files or as Mathematica notebooks (there are 88 of them), all together on a CD accompanying the textbook. The presence of such a collection of numerical analyses enriches the main text and is one of the characteristic features of the book. With the many interesting systems discussed, the book will also be a useful reference for researchers and teachers. It provides the reader with a unique, enjoyable and rather complete textbook of Quantum Mechanics, destined to set a new standard for many years to come.
Quantum mechanics is one of the principle pillars of modern physics. It also remains a topic of great interest to mathematicians. Since its discovery it has inspired and been inspired by many topics within modern mathematics, including functional analysis and operator algebras, Lie groups, Lie algebras and their representations, principle bundles, distribution theory, and much more. Written with beginning graduate students in mathematics in mind, this book provides a thorough treatment of (nonrelativistic) quantum mechanics in a style that is leisurely, without the usual theorem-proof grammar of pure mathematics, while remaining mathematically honest. The author takes the time to fully develop the required mathematics and employs a consistent mathematical presentation to clarify the often-confusing notation of physics texts. Along the way the reader encounters several topics requiring more advanced mathematics than found in many discussions of the subject, making for a fascinating course in how mathematics and physics interact.