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Algebraic Approach to Simple Quantum Systems

With Applications to Perturbation Theory

  • Barry G. Adams

Table of contents

  1. Front Matter
    Pages I-XVI
  2. Barry G. Adams
    Pages 1-15
  3. Barry G. Adams
    Pages 17-23
  4. Barry G. Adams
    Pages 25-40
  5. Barry G. Adams
    Pages 41-79
  6. Barry G. Adams
    Pages 81-104
  7. Barry G. Adams
    Pages 105-117
  8. Barry G. Adams
    Pages 119-136
  9. Barry G. Adams
    Pages 137-177
  10. Barry G. Adams
    Pages 179-209
  11. Barry G. Adams
    Pages 211-244
  12. Barry G. Adams
    Pages 245-246
  13. Barry G. Adams
    Pages 247-260
  14. Barry G. Adams
    Pages 261-264
  15. Barry G. Adams
    Pages 265-280
  16. Barry G. Adams
    Pages 281-294
  17. Barry G. Adams
    Pages 295-312
  18. Barry G. Adams
    Pages 313-330
  19. Barry G. Adams
    Pages 331-353
  20. Barry G. Adams
    Pages 355-378
  21. Barry G. Adams
    Pages 379-433
  22. Back Matter
    Pages 435-451

About this book

Introduction

This book provides an introduction to the use of algebraic methods and sym­ bolic computation for simple quantum systems with applications to large order perturbation theory. It is the first book to integrate Lie algebras, algebraic perturbation theory and symbolic computation in a form suitable for students and researchers in theoretical and computational chemistry and is conveniently divided into two parts. The first part, Chapters 1 to 6, provides a pedagogical introduction to the important Lie algebras so(3), so(2,1), so(4) and so(4,2) needed for the study of simple quantum systems such as the D-dimensional hydrogen atom and harmonic oscillator. This material is suitable for advanced undergraduate and beginning graduate students. Of particular importance is the use of so(2,1) in Chapter 4 as a spectrum generating algebra for several important systems such as the non-relativistic hydrogen atom and the relativistic Klein-Gordon and Dirac equations. This approach provides an interesting and important alternative to the usual textbook approach using series solutions of differential equations.

Keywords

Dirac equation Lie ALgebras Perturbation Theory Quantendynamik Quantenmechanik Quantum System Symbolic Computation Theoretische Chemie quantum mechanics

Authors and affiliations

  • Barry G. Adams
    • 1
  1. 1.Department of Mathematics and Computer ScienceLaurentian UniversitySudburyCanada

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-57933-2
  • Copyright Information Springer-Verlag Berlin Heidelberg 1994
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-57801-7
  • Online ISBN 978-3-642-57933-2
  • Buy this book on publisher's site