Irreducible Tensorial Sets discusses mathematical methods originating from the theory of coupling and recoupling of angular momenta in atomic physics that constitute an extension of vector and tensor algebra. The book presents a unified treatment with a compact system of notations from different approaches, such as group theory, algebra, and quantum mechanical transformation theory. It discusses irreducible tensorial sets that cover different sets of quantities such as tensor components and states of atomic systems. It also explains quantum mechanical applications, coupling and recoupling of atomic and nuclear states, the Wigner-Eckart theorem, and the products of tensorial sets of operators. The text shows how to calculate the interaction energy between atomic systems couple with one another with a constant total angular momentum. The book also explains the correlations which are functions of the Euler angles between the frame of reference in which a radiation is observed and a frame of reference attached to the orienting radiation or field. It then cites sample problems related to the angular distribution of radiations. The book will prove useful for physicists, for mathematicians, or for readers with some knowledge in theoretical physics, particularly on theory of groups and quantum mechanics.
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ISBN-13
978-1-4832-7616-8 (9781483276168)
Schweitzer Klassifikation
Preface 1. IntroductionPart I. Algebra 2. Tensorial Sets 3. Irreducible Sets 4. Transition to Contragredience. Conjugation 5. Standard Sets 6. Invariant Products of Two Sets 7. Irreducible Products of Two Standard Sets. Wigner Coefficients 8. Irreducible Multiple Products of Standard Sets 9. Transformations Between Coupling Schemes 10. Invariant Triple Products. V Coefficients 11. Recoupling of Triple Products. W Coefficients 12. Recoupling of Quadruple Products. X CoefficientsPart II. Quantum Mechanical Applications 13. Coupling and Recoupling of Atomic and Nuclear States 14. Tensorial Sets of Operators. The Wigner-Eckart Theorem 15. Products of Tensorial Sets of Operators 16. Interaction Energy of Coupled Systems 17. Interaction of Coupled Systems with External Fields 18. Reduced Form of Operator Matrices 19. Angular Distribution of RadiationsAppendices A. Group Properties of r-Transformations B. Infinitesimal r-Transformations and Angular Momentum C. Properties of the Matrix U D. Calculation of the Standard r-Transformat ions E. Differential Properties of r-Transformations F. Products of Identical Standard Sets of Degree 1/2 G. Calculation of the Wigner Coefficients H. Diagrams of Recoupling Relationships I. Calculation of W by Recursion Formulas. The Biedenharn Identity J. Tensorial Formulation of the Dipole-Dipole Interaction ("Tensor Force") K. ReferencesSubject Index
