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Whittaker–Hill equation, Ince polynomials, and molecular torsional modes
Author(s) -
Roncaratti Luiz F.,
Aquilanti Vincenzo
Publication year - 2009
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.22255
Subject(s) - mathieu function , polynomial , quantum , transformation (genetics) , variety (cybernetics) , molecule , equations of motion , physics , classical mechanics , mathematical physics , mathematics , chemistry , quantum mechanics , mathematical analysis , biochemistry , statistics , gene
We present an analysis of the Whittaker–Hill equation in view of its usefulness in quantum mechanics when periodic potentials are involved. The transformation due to Ince leads to polynomial solutions which have not attracted much attention so far in the applications. With respect to Mathieu equation, here we have an additional parameter, which permits to describe a variety of phenomena, including the treatment of the torsional motion of flexible molecules. Examples are discussed, with particular attention payed to the case of H 2 O 2 and similar molecules. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010