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Common generating functions of complete harmonic oscillator wave functions and transformation brackets in D dimensions
Author(s) -
ChaosCador L.,
LeyKoo E.
Publication year - 2003
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.10800
Subject(s) - cartesian coordinate system , harmonic oscillator , wave function , transformation (genetics) , coordinate system , mathematics , series (stratigraphy) , harmonic , quantum , quantum harmonic oscillator , generating function , schrödinger equation , physics , mathematical analysis , quantum mechanics , geometry , paleontology , biochemistry , chemistry , biology , gene
The separability of the Schrödinger equation for harmonic oscillators in D dimensions and in different coordinate systems (Cartesian, circular, spherical) makes possible the construction of common generating functions for the complete harmonic oscillator wave functions in the corresponding dimensions and coordinates. Explicit forms of such generating functions and their series expansions are presented, and one of their applications is illustrated through the evaluation of transformation brackets. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004