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Generating functions for oscillator matrix elements
Author(s) -
Witschel W.
Publication year - 1976
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.560100604
Subject(s) - physics , harmonic oscillator , operator (biology) , omega , matrix (chemical analysis) , function (biology) , mathematical physics , combinatorics , mathematics , quantum mechanics , chemistry , biochemistry , repressor , chromatography , evolutionary biology , biology , transcription factor , gene
Two general harmonic oscillator elements \documentclass{article}\pagestyle{empty}\begin{document}$$ \left\langle m \right|\hat x^s \hat p\left| n \right\rangle $$\end{document} and \documentclass{article}\pagestyle{empty}\begin{document}$$ \left\langle m \right|\exp \left[ { - \alpha \left( {\hbar /m*\omega } \right)\hat x^2 } \right]\exp \left( {\beta \hat x} \right)\left| n \right\rangle $$\end{document} are derived by a generating function method using operator techniques which contain practically all one‐ and two‐centre integrals with equal frequencies of chemical physics.