Exact solutions for nonpolynomial potentials in N-space dimensions using a factorization method and supersymmetry
- 1 February 1991
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 32 (2) , 447-456
- https://doi.org/10.1063/1.529432
Abstract
A supersymmetry‐inspired factorization method is used to obtain exact analytic solutions for one or a few quantum states of a broad class of nonpolynomial potentials in an arbitrary space dimension under suitable constraints on the potential parameters. For the specific nonpolynomial oscillator potential, V(x)=x 2+λx 2/(1+g x 2), previous analytic results including algebraic and integral type in one and three dimensions are easily obtainable from these compact expressions. Interesting aspects of the existence of pairs of solutions for certain combinations of λ and g are also discussed.Keywords
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