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Topics in Quantum Mechanics

  • Textbook
  • © 2003

Overview

Authors:
  1. Floyd Williams

    1. Department of Mathematics, University of Massachusetts, Amherst, USA

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Part of the book series: Progress in Mathematical Physics (PMP, volume 27)

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Table of contents (19 chapters)

  1. Front Matter

    Pages i-xv
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  2. Introductory Concepts in Quantum Theory

    1. Front Matter

      Pages 1-1
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    2. Units of Measurement

      • Floyd Williams
      Pages 3-6

    3. Quantum Mechanics: Some Remarks and Themes

      • Floyd Williams
      Pages 7-23

    4. Equations of Motion in Classical Mechanics

      • Floyd Williams
      Pages 25-49

    5. Quantization and the Schrödinger Equation

      • Floyd Williams
      Pages 51-79

    6. Hypergeometric Equations and Special Functions

      • Floyd Williams
      Pages 81-121

    7. Hydrogen-like Atoms

      • Floyd Williams
      Pages 123-155

    8. Heisenberg’s Uncertainty Principle

      • Floyd Williams
      Pages 157-170

    9. Group Representations and Selection Rules

      • Floyd Williams
      Pages 171-216

    10. The Quantized Hamiltonian for a Charged Particle in an Electromagnetic Field

      • Floyd Williams
      Pages 217-231

    11. Spin Wave Functions

      • Floyd Williams
      Pages 233-252

    12. Introduction to Multi-Electron Atoms

      • Floyd Williams
      Pages 253-267

  3. Some Selected Topics

    1. Front Matter

      Pages 269-269
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    2. Fresnel Integrals and Feynman Integrals

      • Floyd Williams
      Pages 271-290

    3. Path Integral for the Harmonic Oscillator

      • Floyd Williams
      Pages 291-297

    4. Euclidean Path Integrals

      • Floyd Williams
      Pages 299-305

    5. The Density Matrix and Partition Function in Quantum Statistical Mechanics

      • Floyd Williams
      Pages 307-315

    6. Zeta Regularization

      • Floyd Williams
      Pages 317-320

    7. Helmholtz Free Energy for Certain Negatively Curved Space-Times, and the Selberg Trace Formula

      • Floyd Williams
      Pages 321-332
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Keywords

About this book

Quantum mechanics and quantum field theory are highly successful physical theo­ ries that have numerous practical applications. Largely mathematical in character, these theories continue to stimulate the imaginations of applied mathematicians and purists as weIl. In recent years, in particular, as a new array of tools have emerged, including a representative amount from the domain of so-called pure mathematics, interest in both the conceptual and physical aspects of these beau­ tiful subjects has especially blossomed. Given the emergence of newer and of­ ten spectacular applications of mathematics to quantum theory, and to theoretical physics in general, one notes that certain communication gaps between physicists and mathematicians continue to be bridged. This text on quantum mechanics, designed primarily for mathematics students and researchers, is an attempt to bridge further gaps. Although the mathematical style presented is generally precise, it is counterbalanced at some points by a re­ laxation of precision, as our overall purpose is to capture the basic fiavor of the subject both formally and intuitively. The approach is one in which we attempt to maintain sensitivity with respect to diverse backgrounds of the readers, including those with modest backgrounds in physics. Thus we have included several con­ crete computational examples to fortify stated principles, several appendices, and certain basic physical concepts that help to provide for a reasonably self-contained account of the material, especially in the first 11 chapters.

Reviews

". . . a number of interesting and classical applications (some involving detailed computations) are included. Most of the book is dedicated to covering the traditional material but there are also some innovations, both in the choice of topics and in the way they are presented. . . . overall, I shall say that this is a very good text that is welcome both from the conceptual and the operational points of view. The theoretical physics community should also find here a good source on the subject."

—Mathematical Reviews

Authors and Affiliations

  • Department of Mathematics, University of Massachusetts, Amherst, USA

    Floyd Williams

Bibliographic Information

  • Book Title: Topics in Quantum Mechanics

  • Authors: Floyd Williams

  • Series Title: Progress in Mathematical Physics

  • DOI: https://doi.org/10.1007/978-1-4612-0009-3

  • Publisher: Birkhäuser Boston, MA

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 2003

  • Hardcover ISBN: 978-0-8176-4311-9Published: 23 January 2003

  • Softcover ISBN: 978-1-4612-6571-9Published: 23 October 2012

  • eBook ISBN: 978-1-4612-0009-3Published: 06 December 2012

  • Series ISSN: 1544-9998

  • Series E-ISSN: 2197-1846

  • Edition Number: 1

  • Number of Pages: XV, 398

  • Number of Illustrations: 1 b/w illustrations

  • Topics: Number Theory, Topological Groups, Lie Groups, Analysis, Quantum Physics

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