β Scribed by C. A. Morrison (auth.)
No coin nor oath required. For personal study only.
From December 1985 through March 1986 the text of this book formed the basis of an in-hours course taught by the author at Harry Diamond LaboratoΒ ries. Considerable assistance in revising and organizing the first draft was given by John Bruno. The original draft of these notes was based on a collection of lectures delivered at the Universidade Federal de Pernambuco, Recife, Brazil, between 2 November 1981 and 2 December 1981. The visit to Recife was a response to an invi tation of Professor Gilberto F. de Sa of the Physics Department. In the preparation of these notes I made many requests of my coworkers for earlier resul ts and recollections of our early work. Among those consul ted were Donald Wortman, Nick Karayianis, and Richard Leavitt. Further, a number of .suggestions from my Brazilian colleagues helped make the lectures more clear. Particular among these were Professor Oscar Malta and Professor Alfredo A. da Gama both of whom I wish to thank for their help. Encouragement and assistance with funding for much of this work came from Leon Esterowitz of the Naval Research Laboratory and Rudolph Buser and Albert Pinto of the center for Night Vision and Electro-Optics.
Front Matter....Pages N2-8
Introduction and Review of Previous Literature....Pages 9-18
Clebsch-Gordan Coefficients....Pages 19-23
Wigner-Eckart Theorem....Pages 24-34
Unit Spherical Tensors....Pages 35-38
Racah Coefficients....Pages 39-48
Racah Algebra....Pages 49-65
Free-Ion Hamiltonian Unfilled Configuration nβ N [N < 2(2β + 1)]....Pages 66-80
Crystal-Field Interactions--Phenomenological Theory of Crystal Fields....Pages 81-88
Matrix Elements of H 3 in Total Angular Momentum States for the Electronic Configuration nβ N ....Pages 89-92
Group Theoretical Considerations....Pages 93-102
Numerical Example: 4 F J States of Nd 3+ (4f 3 )....Pages 103-110
Classical Point-Charge Model....Pages 111-118
Point-Charge Model Developed at HDL....Pages 119-127
Crystal-Field Effects not yet Fully Incorporated....Pages 128-142
Miscellaneous Crystal-Field Effects....Pages 143-152
Back Matter....Pages 153-161
Theoretical and Computational Chemistry;Physical Chemistry;Inorganic Chemistry;Laser Technology, Photonics;Quantum Optics
π SIMILAR VOLUMES
This 1985 text develops the theory of angular momentum from the viewpoint of a fundamental symmetry in nature and shows how this concept relates to applied areas of research in modern quantum physics
This is four papers of P. Winternitz and co-authors which link separation of variables in differential equations with its symmetry group. Here ii abstract of these papers: On Relativistic Angular Momentum Theory P. Winternitz, Ya. A. Smorodinskii, and M. Uhlir Soviet Journal of Nuclear Physics:
<p><P>Application of quantum mechanics in physics and chemistry often entails manipulation and evaluation of sums and products of coupling coefficients for the theory of angular momentum. Challenges encountered in such work can be tamed by graphical techniques that provide both the insight and analy