An Introduction to Hilbert Space and Quantum Logic

  • David W. Cohen

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

Table of contents

  1. Front Matter
    Pages i-xii
  2. David W. Cohen
    Pages 1-13
  3. David W. Cohen
    Pages 14-20
  4. David W. Cohen
    Pages 21-42
  5. David W. Cohen
    Pages 43-48
  6. David W. Cohen
    Pages 49-59
  7. David W. Cohen
    Pages 60-72
  8. David W. Cohen
    Pages 73-84
  9. Back Matter
    Pages 147-149

About this book

Introduction

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.

Keywords

Functionals algebra development eigenvalue experiment geometry influence mathematics mechanics momentum physics quantum mechanics solution spectra

Authors and affiliations

  • David W. Cohen
    • 1
  1. 1.Department of MathematicsSmith CollegeNorthamptonUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4613-8841-8
  • Copyright Information Springer-Verlag New York 1989
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4613-8843-2
  • Online ISBN 978-1-4613-8841-8
  • Series Print ISSN 0941-3502
  • About this book