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Bender–Wu formulas and classical trajectories: Higher dimensions and degeneracies
Author(s) -
Avron J. E.
Publication year - 1982
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.560210108
Subject(s) - degenerate energy levels , zeeman effect , eigenvalues and eigenvectors , separable space , perturbation (astronomy) , hamiltonian (control theory) , mathematical physics , series (stratigraphy) , physics , classical mechanics , mathematics , mathematical analysis , quantum mechanics , magnetic field , mathematical optimization , paleontology , biology
A method for the asymptotics of the perturbation series (Bender‐Wu formulas) which is not restricted to one dimension is outlined. The method has a classical mechanic flavor and involves computing classical trajectories using classical perturbation methods. The method applies also when the unperturbed eigenvalues are degenerate. It is illustrated for the Hydrogen Zeeman Hamiltonian which is not separable and has degeneracies.