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Algebraic Approach to Simple Quantum Systems

With Applications to Perturbation Theory

  • Textbook
  • © 1994

Overview

Authors:
  1. Barry G. Adams

    1. Department of Mathematics and Computer Science, Laurentian University, Sudbury, Canada

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Table of contents (20 chapters)

  1. Front Matter

    Pages I-XVI
    Download chapter PDF

  2. General Discussion of Lie Algebras

    • Barry G. Adams
    Pages 1-15

  3. Commutator Gymnastics

    • Barry G. Adams
    Pages 17-23

  4. Angular Momentum Theory and so(3)

    • Barry G. Adams
    Pages 25-40

  5. Representations and Realizations of so(2,1)

    • Barry G. Adams
    Pages 41-79

  6. Representations and Realizations of so(4)

    • Barry G. Adams
    Pages 81-104

  7. Scaled Hydrogenic Realization of so(4,2)

    • Barry G. Adams
    Pages 105-117

  8. Lie Algebraic Perturbation Theory

    • Barry G. Adams
    Pages 119-136

  9. Symbolic Calculation of the Stark Effect

    • Barry G. Adams
    Pages 137-177

  10. Symbolic Calculation of the Zeeman Effect

    • Barry G. Adams
    Pages 179-209

  11. Spherically Symmetric Systems

    • Barry G. Adams
    Pages 211-244

  12. The Levi-Civita Symbol

    • Barry G. Adams
    Pages 245-246

  13. Lie Groups and Lie Algebras

    • Barry G. Adams
    Pages 247-260

  14. The Tilting Transformation

    • Barry G. Adams
    Pages 261-264

  15. Perturbation Matrix Elements

    • Barry G. Adams
    Pages 265-280

  16. Tables of Stark Effect Energy Corrections

    • Barry G. Adams
    Pages 281-294

  17. Tables of Zeeman Effect Energy Corrections

    • Barry G. Adams
    Pages 295-312

  18. Tables of Charmonium Energy Corrections

    • Barry G. Adams
    Pages 313-330

  19. Tables of Harmonium Energy Corrections

    • Barry G. Adams
    Pages 331-353

  20. Tables of Screened Coulomb Energy Corrections

    • Barry G. Adams
    Pages 355-378
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Mathematics and Computer Science, Laurentian University, Sudbury, Canada

    Barry G. Adams

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