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Invariant Harmonic Oscillator Functions. I. The Cubic Groups T d , O, and O h
Author(s) -
Wöhlecke M.,
Scherz U.,
Maretis D. K.
Publication year - 1985
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2221300111
Subject(s) - harmonic oscillator , irreducible representation , invariant (physics) , symmetry group , excited state , wave function , mathematics , computation , direct product , quantum harmonic oscillator , quantum mechanics , pure mathematics , mathematical physics , physics , geometry , algorithm
Excited energy states of quantum mechanical two‐ or three‐dimensional harmonic oscillators are of interest in Jahn‐Teller calculations and rotational tunneling systems. A general method is given to calculate symmetry adapted oscillator functions by numerical computation. The basic relations are formulated in the occupation number representation. Therefore advantage of group properties like isomorphism and direct product groups can be taken easily. Results are given for two‐ and three‐dimensional irreducible representations of the cubic groups O h , O, and T d .