Abstract
The exact solutions of wave equations are possible only for a few potentials. We have to use some approximation methods to obtain their solutions. Until now, many efforts have been made to solve the stationary Schrödinger equation with the anharmonic potentials containing negative powers of the radial coordinate. Interest in them stems from the fact that the study of the Schrödinger equation with these potentials provides us for insight into the physical problem. However, most of those works have been mainly carried out in the lower-dimensional space. The purpose of this Chapter is, by applying a suitable ansatz to the wavefunction, to analyze the D-dimensional radial Schrödinger equation with anharmonic potentials such as the sextic potential V(r)=ar 6+br 4+cr 2, the singular integer power potentials V(r)=ar 2+br −2+cr −4+dr −6, the singular fraction power potentials V(r)=ar −1/2+br −3/2 and others.
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Dong, SH. (2011). Wavefunction Ansatz Method. In: Wave Equations in Higher Dimensions. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-1917-0_8
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