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N-dimensional electron in a spherical potential: the large-N limit

Amit K Chattopadhyay
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Abstract

We show that the energy levels predicted by a 1/N-expansion method for an N-dimensional Hydrogen atom in a spherical potential are always lower than the exact energy levels but monotonically converge towards their exact eigenstates for higher ordered corrections. The technique allows a systematic approach for quantum many body problems in a confined potential and explains the remarkable agreement of such approximate theories when compared to the exact numerical spectrum.

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Amit K Chattopadhyay. 2006-01-19. N-dimensional electron in a spherical potential: the large-N limit. https://doi.org/10.1016/j.physleta.2006.04.028

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