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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
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