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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Dong et al. (2004) studied this question.
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