Study of a class of non-polynomial oscillator potentials

Details Study of a class of non-polynomial oscillator potentials Study of a class of non-polynomial oscillator potentials

2006-05-18

arxiv.org/abs/math-ph/0605056v1

J. Phys. A 39, 7745 - 7756 (2006)

Physics

Mathematical Physics

16 pages

Scientific paper

10.1088/0305-4470/39/24/011

We develop a variational method to obtain accurate bounds for the eigenenergies of H = -Delta + V in arbitrary dimensions N>1, where V(r) is the nonpolynomial oscillator potential V(r) = r^2 + lambda r^2/(1+gr^2), lambda in (-infinity,\infinity), g>0. The variational bounds are compared with results previously obtained in the literature. An infinite set of exact solutions is also obtained and used as a source of comparison eigenvalues.

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