Study of a class of non-polynomial oscillator potentials
Nasser Saad, Richard L. Hall, Hakan Ciftci
Abstract
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) = r2 + lambda r2/(1+gr2), lambda in (-infinity,∈finity), 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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