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Harmonic oscillator tensors. II. angular momentum expressions of matrix elements of vibrational operators
Author(s) -
Palting Pancracio
Publication year - 1993
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560460204
Subject(s) - angular momentum , harmonic oscillator , creation and annihilation operators , angular momentum operator , total angular momentum quantum number , clebsch–gordan coefficients , homogeneous space , angular momentum coupling , irreducible representation , physics , matrix (chemical analysis) , mathematical physics , quantum mechanics , mathematics , quantum , chemistry , geometry , chromatography
Abstract The spatial symmetries of the harmonic oscillator and the recently found irreducible tensors constructed from the associated annihilation and creation operators are exploited to obtain new expressions for the elements of the matrix representatives of several examples of vibrational operators. Since all vibrational operators are expressible in terms of the irreducible tensors, their matrix elements reflect the angular momentum symmetry inherent in them, for the results derived here are in terms of the Clebsch–Gordan coefficients and the isoscalar factors that arise from the couplinig rule of the irreducible tensors. Familiarity with the mathematical properties of these quantities derived from the elementary theory of angular momentum facilitates the evaluation of many vibrational operators that may be of importance in the study of potentials in this basis. In particular, it is shown that the nonvanishing of matrix elements is governed by a law of conservation of angular momentum along the axis of quantization of the nondegenerate harmonic oscillator. © 1993 John Wiley & Sons, Inc.