## Exact solutions of the two-dimensional Schrödinger equation with certain central potentials.(English)Zbl 0985.81028

Summary: By applying an ansatz to the eigenfunction, an exact closed-form solution of the Schrödinger equation in two dimensions is obtained with the potentials $$V(r)= ar^2+ br^4+ cr^6$$, $$V(r)= ar+ br^2+ cr^{-1}$$, and $$V(r)= ar^2+ br^{-2}+ cr^{-4}+ dr^{-6}$$, respectively. The restrictions on the parameters of the given potential and the angular momentum $$m$$ are obtained.

### MSC:

 81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics

### Keywords:

restrictions on the parameters; angular momentum
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