Research Catalog

Title

Algebraic approach to simple quantum systems : with applications to perturbation theory / Barry G. Adams.

Author

Adams, Barry G.

Publication

Berlin ; New York : Springer-Verlag, [1994], ©1994.

Items in the Library & Off-site

Holdings

Details

Description

xvi, 451 pages; 24 cm +

Summary

• This monograph is primarily aimed at advanced undergraduates and first-year graduate students and researchers in theoretical and computational chemistry. It will also be useful to researchers in mathematical physics. It is the first book to systematically explore the application of Lie algebraic methods to simple quantum systems and perturbation theory with an emphasis on symbolic computation. Many exercises complete with solutions are also included.
• In the first part of the book the basic concepts of Lie algebras are presented in a pedagogical manner, first in the familiar context of angular momentum theory, and then for the important Lie algebras so (2,1), so (4) and so(4,2).
• Next, a novel feature is the application of the algebraic methods to obtain the energy and wavefunctions of the standard textbook problems of the non-relativistic and relativistic hydrogenic atoms and the harmonic oscillator. This provides an elegant and algebraic alternative to the usual approach using series solutions of differential equations.
• In the second part of the book applications of these algebraic methods to large order algebraic perturbation theory are considered for the Stark and Zeeman effect and spherically symmetric systems with charmonium, harmonium and screened Coulomb perturbations using the Maple computer algebra system. Application of the Hellman-Feynman and Hypervirial theorems to the perturbation theory of spherically symmetric systems is also considered using Maple.
• A disk containing Maple programs and data files is also included.

Subject

• Perturbation (Quantum dynamics)
• Lie algebras
• Chemistry, Physical and theoretical
• Mathematical physics

Note

• System requirements for computer disk: IBM-compatible PC; DOS.

Bibliography (note)

• Includes bibliographical references (p. [435]-442) and indexes.

Contents

1. General Discussion of Lie Algebras -- 2. Commutator Gymnastics -- 3. Angular Momentum Theory and so(3) -- 4. Representations and Realizations of so(2,1) -- 5. Representations and Realizations of so(4) -- 6. Scaled Hydrogenic Realization of so(4,2) -- 7. Lie Algebraic Perturbation Theory -- 8. Symbolic Calculation of the Stark Effect -- 9. Symbolic Calculation of the Zeeman Effect -- 10. Spherically Symmetric Systems -- A The Levi-Civita Symbol -- B Lie Groups and Lie Algebras -- C The Tilting Transformation -- D Perturbation Matrix Elements -- E Tables of Stark Effect Energy Corrections -- F Tables of Zeeman Effect Energy Corrections -- G Tables of Charmonium Energy Corrections -- H Tables of Harmonium Energy Corrections -- I Tables of Screened Coulomb Energy Corrections -- J Solutions to Exercises.

ISBN

• 3540578013 (Berlin : acid-free)
• 0387578013 (New York : acid-free)

LCCN

94011900

OCLC

• 30155631
• ocm30155631

Owning Institutions

Columbia University Libraries