Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2007-02-20
AnnalsPhys.323:1424-1459,2008
Physics
High Energy Physics
High Energy Physics - Theory
29 pages, 5 figures
Scientific paper
10.1016/j.aop.2007.11.006
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 ratios of three distance scales of the trial wavefunctions. The energies of the ground state and the first order excited state, in the $0^{th}$ 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.
Kim Hyeong-Chan
Yee Jae Hyung
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