Applications of Group Theory in Quantum Mechanics - Brossura

Petrashen, M. I.; Trifonov, E. D.

Brossura

ISBN 10: 048647223X ISBN 13: 9780486472232

Casa editrice: Dover Pubns, 2009

Riassunto

Geared toward postgraduate students, theoretical physicists, and researchers, this advanced text explores the role of modern group-theoretical methods in quantum theory. The authors based their text on a physics course they taught at a prominent Soviet university. Readers will find it a lucid guide to group theory and matrix representations that develops concepts to the level required for applications.
The text's main focus rests upon point and space groups, with applications to electronic and vibrational states. Additional topics include continuous rotation groups, permutation groups, and Lorentz groups. A number of problems involve studies of the symmetry properties of the Schroedinger wave function, as well as the explanation of "additional" degeneracy in the Coulomb field and certain subjects in solid-state physics. The text concludes with an instructive account of problems related to the conditions for relativistic invariance in quantum theory.

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Contenuti:

Foreword Introduction Abstract Groups Representations of Point Groups Composition of Representations and the Direct Products of Groups Wigner's Theorem Point Groups Decomposition of a Reducible Representation into an Irreducible Representation Space Groups and their Irreducible Representations Classification of the Vibrational and Electronic States of a Crystal Continuous Groups Irreducible Representations of the Three-Dimensional Rotation Group The Properties of Irreducible Representations of the Rotation Group Some Applications of the Theory of Representation of the Rotation Group in Quantum Mechanics Additional Degeneracy in a Spherically Symmetric Field Permutation Groups Symmetrized Powers of Representations Symmetry Properties of Multi-Electron Wave Functions Symmetry Properties of Wave Functions for a System of Identical Particles with Arbitrary Spins Classification of the States of a Multi-Electron Atom Applications of Group Theory to Problems Connected with the Perturbation Theory Selection Rules The Lorentz Group and its Irreducible Representations The Dirac Equation Appendix to Chapter 7 Bibliography Index

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• Editore: Dover Pubns
• Data di pubblicazione: 2009
• ISBN 10: 048647223X
• ISBN 13: 9780486472232
• Rilegatura: Copertina flessibile
• Numero di pagine: 318