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Renormalized perturbation theory by the moment method for degenerate states: Anharmonic oscillators
Author(s) -
Radicioni Marcelo D.,
Diaz Carlos G.,
Fernández Francisco M.
Publication year - 1998
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/(sici)1097-461x(1998)66:4<261::aid-qua1>3.0.co;2-t
Subject(s) - anharmonicity , degenerate energy levels , eigenfunction , eigenvalues and eigenvectors , perturbation (astronomy) , perturbation theory (quantum mechanics) , physics , quantum mechanics , poincaré–lindstedt method , quantum , harmonic oscillator , hamiltonian (control theory) , transition of state , quantum electrodynamics , mathematical physics , mathematics , coherent states , mathematical optimization
We apply renormalized perturbation theory by the moment method to an anharmonic oscillator in two dimensions with a perturbation that couples unperturbed degenerate states. The method leads to simple recurrence relations for the perturbation corrections to the energy and moments of the eigenfunction. We calculate accurate energy eigenvalues, illustrate the general features of the method, and comment on the application of the approach to other quantum mechanical models. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 66 : 261–272, 1998