Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physics Bulletin

Quantum Mechanics in Hilbert Space

Alan Cottey

Published Mar 1, 1972• 77 citations
Publisher

Abstract

Eduard Prugovecki London: Academic Press 1971 pp xv + 648 price £13·75 The first half of this book is devoted to the theory of Hilbert space and linear operators in Hilbert space, with a little reference to quantum mechanics. The second half deals in detail with two topics in quantum mechanics, namely the axiomatic structure of quantum mechanics, and scattering theory.

DOI
10.1088/0031-9112/23/3/018

Related papers

Quantum Mechanics in Hilbert Space (Eduard Prugovecki)

J.M. Cook

Previous article Next article Quantum Mechanics in Hilbert Space (Eduard Prugovecki)J. M. CookJ. M. Cookhttps://doi.org/10.1137/1015056PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout"Quantum Mechanics in Hilbert Space (Eduard Prugovecki)." SIAM Review, 15(2), pp. 403–404 Previous article Next article FiguresRelatedReferencesCited byDetails Volume 15, Issue 2| 1973SIAM Review History Published online:02 August 2006 InformationCopyright © 1973 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1015056Article page range:pp. 403-404ISSN (print):0036-1445ISSN (online):1095-7200Publisher:Society for Industrial and Applied Mathematics

SIAM Review•Apr 1, 1973•0 citations

Problems in Quantum Mechanics

R. C. Johnson

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).

Physics Bulletin•Sep 1, 1971•46 citations

Techniques of Applied Quantum Mechanics

John Ewan Inglesfield

J P Killingbeck London: Butterworths 1975 pp 224 price £9 The title of this book is somewhat misleading (as the author himself admits) because half the book is about the mathematical background to Hilbert spaces and all that – interesting, but I doubt if many readers will be tempted to venture any deeper into Hilbert space. The rest of the book, about perturbation methods and group theory is useful, and has destroyed some of my misconceptions about the convergence of perturbation series.

Physics Bulletin•Jun 1, 1976•20 citations

Problems in Quantum Mechanics

Lewis Elton

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.

Physics Bulletin•May 1, 1961•94 citations

Quantum Mechanics

Yorick Hardy, Willi-Hans Steeb

In this chapter we introduce the Hilbert space which plays the central role in quantum mechanics. For a more detailed discussion of this subject we refer to the books of Balakrishnan [5], Richtmyer [137], Sewell [146], Stakgold [152], Steeb [163], Weidmann [181], Yosida [185]. Moreover the proofs of the theorems given in this chapter can be found in these books. We assume that the reader is familiar with the notation of a linear space. First we introduce the pre-Hilbert space. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Birkhäuser Basel eBooks•Jan 1, 2001•6 citations

Quantum mechanics

Peter Szekeres

Our purpose in this chapter is to present the key concepts of quantum mechanics in the language of Hilbert spaces. The reader who has not previously met the physical ideas motivating quantum mechanics, and some of the more elementary applications of Schrödinger's equation, is encouraged to read any of a number of excellent texts on the subject such as [1–4]. Otherwise, the statements given here must to a large extent be taken on trust – not an altogether easy thing to do, since the basic assertions of quantum theory are frequently counterintuitive to anyone steeped in the classical view of physics. Quantum mechanics is frequently presented in the form of several postulates, as though it were an axiomatic system such as Euclidean geometry. As often presented, these postulates may not meet the standards of mathematical rigour required for a strictly logical set of axioms, so that little is gained by such an approach. We will do things a little more informally here. For those only interested in the mathematical aspects of quantum mechanics and the role of Hilbert space see [5–8]. Many of the standard applications, such as the hydrogen atom, will be omitted here as they can be found in all standard textbooks, and we leave aside the enormous topic of measurement theory and interpretations of quantum mechanics. This is not to say that we need be totally comfortable with quantum theory as it stands. Undoubtedly, there are some philosophically disquieting features in the theory, often expressed in the form of socalled paradoxes.

Cambridge University Press eBooks•Dec 16, 2004•0 citations
Eduard Prugovecki London: Academic Press 1971 pp xv + 648 price £13·75 The first half of this book is devoted to the theory of Hilbert space and linear operators in Hilbert space, with a little reference to quantum mechanics. The second half deals in detail with two topics in quantum mechanics, namely the axiomatic structure of quantum mechanics, and scattering theory.
Previous article Next article Quantum Mechanics in Hilbert Space (Eduard Prugovecki)J. M. CookJ. M. Cookhttps://doi.org/10.1137/1015056PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout"Quantum Mechanics in Hilbert Space (Eduard Prugovecki)." SIAM Review, 15(2), pp. 403–404 Previous article Next article FiguresRelatedReferencesCited byDetails Volume 15, Issue 2| 1973SIAM Review History Published online:02 August 2006 InformationCopyright © 1973 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1015056Article page range:pp. 403-404ISSN (print):0036-1445ISSN (online):1095-7200Publisher:Society for Industrial and Applied Mathematics
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.
In this chapter we introduce the Hilbert space which plays the central role in quantum mechanics. For a more detailed discussion of this subject we refer to the books of Balakrishnan [5], Richtmyer [137], Sewell [146], Stakgold [152], Steeb [163], Weidmann [181], Yosida [185]. Moreover the proofs of the theorems given in this chapter can be found in these books. We assume that the reader is familiar with the notation of a linear space. First we introduce the pre-Hilbert space. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Our purpose in this chapter is to present the key concepts of quantum mechanics in the language of Hilbert spaces. The reader who has not previously met the physical ideas motivating quantum mechanics, and some of the more elementary applications of Schrödinger's equation, is encouraged to read any of a number of excellent texts on the subject such as [1–4]. Otherwise, the statements given here must to a large extent be taken on trust – not an altogether easy thing to do, since the basic assertions of quantum theory are frequently counterintuitive to anyone steeped in the classical view of physics. Quantum mechanics is frequently presented in the form of several postulates, as though it were an axiomatic system such as Euclidean geometry. As often presented, these postulates may not meet the standards of mathematical rigour required for a strictly logical set of axioms, so that little is gained by such an approach. We will do things a little more informally here. For those only interested in the mathematical aspects of quantum mechanics and the role of Hilbert space see [5–8]. Many of the standard applications, such as the hydrogen atom, will be omitted here as they can be found in all standard textbooks, and we leave aside the enormous topic of measurement theory and interpretations of quantum mechanics. This is not to say that we need be totally comfortable with quantum theory as it stands. Undoubtedly, there are some philosophically disquieting features in the theory, often expressed in the form of socalled paradoxes.