Article ID Journal Published Year Pages File Type
1857700 Annals of Physics 2008 36 Pages PDF
Abstract

We propose a variational perturbation method based on the observation that eigenvalues of each parity sector of both the anharmonic and double-well oscillators are approximately equi-distanced. The generalized deformed algebra satisfied by the invariant operators of the systems provides well defined Hilbert spaces to both of the oscillators. There appears a natural expansion parameter defined by the ratio of length scales of the trial wavefunctions. The energies of the ground state and the first order excited state, in the zeroth order variational approximation, are obtained with errors <10−2% for vast range of the coupling strength for both oscillators. An iterative formula is presented which perturbatively generates higher order corrections from the lower order invariant operators and the first order correction is explicitly given.

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Physical Sciences and Engineering Physics and Astronomy Physics and Astronomy (General)
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