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Algebraic Approach to Simple Quantum Systems : With Applications to Perturbation Theory - Barry G. Adams

Algebraic Approach to Simple Quantum Systems : With Applications to Perturbation Theory

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The author aims this text primarily at advanced undergraduates and first-year graduate students in theoretical and computational chemistry. The text begins with a pedagogic introduction to the Lie algebras needed for the study of simple quantum systems such as the N-dimensional hydrogen atom and the harmonic oscillator. The second part presents applications of these algebraic methods to the large order perturbation theory of Stark, Zeeman and spherically symmetric perturbation potentials, using symbolic computation and the Maple computer algebra system. A diskette containing the programs and datafiles from the book's problems and examples is included.

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.- Index of Symbols Used.

ISBN: 9783540578017
ISBN-10: 3540578013
Audience: Tertiary; University or College
Format: Book with Other Items
Language: English
Number Of Pages: 451
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.5 x 15.5  x 2.4
Weight (kg): 0.73