Elementary Theory of Angular Momentum: (Dover Books on Physics)

A crucial element in the development of physical theories of nuclear and atomic structure, the theory of angular momentum can be applied with great effect to the formulation and solution of problems associated with the static magnetic and electric nuclear moments which are coupled to the electric and magnetic fields arising from surrounding charges. The theory relates to a variety of physical problems including those associated with low-temperature studies and microwave spectroscopy.This high-level treatment, based on a series of lectures the author gave at Oak Ridge National Laboratory, offers clear discussions of the general theory and its applications. Beginning with basic principles, the development is carried through the introduction of coupling coefficients for vector addition, the transformation properties of the angular momentum wave functions under rotations of the coordinate axes, irreducible tensors and Racah coefficients. Applications include static moments of systems composed schemes in nuclear reactions and more. In this volume, the author has attempted to achieve simplification by concerning himself only with the properties of rotations because of their intimate connection with the concept of angular momentum. In addition, the reasoning is inductive, and, as the theory initially develops, it makes a ""smooth-join"" with those aspects of quantum mechanics that are, comparatively speaking, common knowledge. A graduate-level knowledge of quantum mechanics is helpful for gaining maximum benefit from this highly regarded study.

Table of Contents:
Part A. GENERAL THEORY I. REVIEW OF BASIC PRINCIPLES 1. HERMITIAN OPERATORS 2. UNITARY TRANSFORMATIONS 3. DIAGONALIZATION OF OPERATORS 4. EXPONENTIAL FORM OF THE UNITARY OPERATORS II. THE ANGULAR MOMENTUM OPERATORS 5. DEFINITION OF ANGULAR MOMENTUM OPERATORS 6. ORBITAL ANGULAR MOMENTUM 7. COMMUTATION RULES FOR ANGULAR MOMENTUM OPERATORS 8. EIGENVALUES OF THE ANGULAR MOMENTUM OPERATORS 9. PHYSICAL INTERPRETATION OF ANGULAR MOMENTUM III. COUPLING OF TWO ANGULAR MOMENTA 10. DEFINITION OF THE CLEBSCH-GORDAN COEFFICIENTS 11. SYMMETRY RELATIONS OF THE CLEBSCH-GORDAN COEFFICIENTS 12. EVALUATION OF CLEBSCH-GORDAN COEFFICIENTS IV. TRANSFORMATION PROPERTIES UNDER ROTATIONS 13. MATRIX REPRESENTATIONS OF THE ROTATION OPERATORS 14. THE CLEBSCH-GORDAN SERIES 15. DETERMINATION OF THE ROTATION MATRICES 16. ORTHOGONALITY AND NORMALIZATION OF THE ROTATION MATRICES V. IRREDUCIBLE TENSORS 17. DEFINITION OF IRREDUCIBLE TENSOR OPERATORS 18. RACAH'S DEFINITION OF IRREDUCIBLE TENSOR OPERATORS 19. THE WIGNER-ECKART THEOREM 20. THE PROJECTION THEOREM FOR FIRST-RANK TENSORS 21. ANGULAR MOMENTUM OF A VECTOR FIELD VI. RACAH COEFFICIENTS 22. COUPLING OF THREE ANGULAR MOMENTA 23. PROPERTIES OF THE RACAH COEFFICIENTS 24. BASIC APPLICATIONS 25. THE GRADIENT FORMULA Part B. APPLICATIONS VII. THE ELECTROMAGNETIC FIELD 26. THE MAXWELL EQUATIONS 27. THE MULTIPOLE FIELDS VIII. STATIC INTERACTIONS 28. MULTIPOLE MOMENTS OF AN ELECTROSTATIC CHARGE DISTRIBUTION 29. SPIN INTERACTIONS IX. PARTICLES OF SPIN 1/2 30. NON-RELATIVISTIC DESCRIPTION 31. RELATIVISTIC DESCRIPTION X. ORIENTED NUCLEI AND ANGULAR CORRELATIONS 32. CAPTURE OF POLARIZED NEUTRONS BY POLARIZED NUCLEI 33. ANGULAR CORRELATION 34. EMISSION OF ALPHA PARTICLES BY AN ORIENTED NUCLEUS XI. ANGULAR DISTRIBUTIONS IN NUCLEAR REACTIONS 35. j-j AND L-S COUPLING 36. ANGULAR MOMENTUM COUPLING IN NUCLEAR REACTIONS XII. IDENTICAL PARTICLES 37. IDENTICAL PARTICLES IN j-j COUPLING 38. IDENTICAL PARTICLES IN L-S COUPLING 39. THE ISOTOPIC SPIN APPENDIX I. CLEBSCH-GORDAN AND RACAH COEFFICIENTS APPENDIX II. THE ROTATION MATRICES APPENDIX III. THE SPHERICAL HARMONICS AUTHOR INDEX SUBJECT INDEX