The Schrödinger Equation with a Coulomb Plus Inverse-Square Potential in D Dimensions

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Published under licence by IOP Publishing Ltd
, , Citation Shi-Hai Dong and Guo-Hua Sun 2004 Phys. Scr. 70 94 DOI 10.1088/0031-8949/70/2-3/004

1402-4896/70/2-3/94

Abstract

A D-dimensional Schrödinger equation with a Coulomb plus inverse-square potential is carried out. The relationship between the energy E(n,l,D) and the dimension D is analyzed in great detail. It is shown that the E(n,0,D) first decreases for D ∊ (0,2] and then increases for D ≥ 2. The energy E(n,l,D) is almost independent of the quantum number l for large D, but the quantum number l plays some role in the energy E(n,l,D) when the dimension D is not too large.

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10.1088/0031-8949/70/2-3/004