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  • Textbook
  • © 1989

An Introduction to Hilbert Space and Quantum Logic

Authors:

  1. David W. Cohen

    1. Department of Mathematics, Smith College, Northampton, USA

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Part of the book series: Problem Books in Mathematics (PBM)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xii
    PDF

  2. Experiments, Measure and Integration

    • David W. Cohen
    Pages 1-13

  3. Hilbert Space Basics

    • David W. Cohen
    Pages 14-20

  4. The Logic of Nonclassical Physics

    • David W. Cohen
    Pages 21-42

  5. Subspaces in Hilbert Space

    • David W. Cohen
    Pages 43-48

  6. Maps on Hilbert Spaces

    • David W. Cohen
    Pages 49-59

  7. State Space and Gleason’s Theorem

    • David W. Cohen
    Pages 60-72

  8. Spectrality

    • David W. Cohen
    Pages 73-84

  10. Back Matter

    Pages 147-149
    PDF
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About this book

Historically, nonclassical physics developed in three stages. First came a collection of ad hoc assumptions and then a cookbook of equations known as "quantum mechanics". The equations and their philosophical underpinnings were then collected into a model based on the mathematics of Hilbert space. From the Hilbert space model came the abstaction of "quantum logics". This book explores all three stages, but not in historical order. Instead, in an effort to illustrate how physics and abstract mathematics influence each other we hop back and forth between a purely mathematical development of Hilbert space, and a physically motivated definition of a logic, partially linking the two throughout, and then bringing them together at the deepest level in the last two chapters. This book should be accessible to undergraduate and beginning graduate students in both mathematics and physics. The only strict prerequisites are calculus and linear algebra, but the level of mathematical sophistication assumes at least one or two intermediate courses, for example in mathematical analysis or advanced calculus. No background in physics is assumed.
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Keywords

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Authors and Affiliations

  • Department of Mathematics, Smith College, Northampton, USA

    David W. Cohen

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Bibliographic Information

  • Book Title: An Introduction to Hilbert Space and Quantum Logic

  • Authors: David W. Cohen

  • Series Title: Problem Books in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4613-8841-8

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York Inc. 1989

  • Softcover ISBN: 978-1-4613-8843-2Published: 12 October 2011

  • eBook ISBN: 978-1-4613-8841-8Published: 06 December 2012

  • Series ISSN: 0941-3502

  • Series E-ISSN: 2197-8506

  • Edition Number: 1

  • Number of Pages: XII, 149

  • Topics: Theoretical, Mathematical and Computational Physics

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Buy it now

eBook USD 69.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 89.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

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