Exact solution of the Schrödinger equation for the central nonpolynomial potential \(V(r)=r^ 2+\lambda r^ 2/(1+gr^ 2)\) in two and three dimensions. (English) Zbl 0725.34010
Author’s abstract: “We derive a class of exact solutions of the Schrödinger equation for the central nonpolynomial potential \(V(r)=r^ 2+\lambda r^ 2/(1+gr^ 2)\) in two and three dimensions. This potential is relevant in the context of laser physics. The eigenfunctions and eigenvalues obtained here may, therefore, be useful for applications in lasers.”
Reviewer: J.Ohriska (Košice)
MSC:
| 34A25 | Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. |
| 34A05 | Explicit solutions, first integrals of ordinary differential equations |
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
| 34L40 | Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) |
| 78A60 | Lasers, masers, optical bistability, nonlinear optics |
