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

TL;DR

This paper demonstrates that a 1/N-expansion method provides systematically improving lower bounds for the energy levels of an N-dimensional hydrogen atom in a spherical potential, converging towards the exact energies.

Contribution

It introduces a systematic 1/N-expansion technique for approximating energy levels in N-dimensional quantum systems, explaining its accuracy and convergence.

Findings

Energy levels are always underestimated by the 1/N-expansion.

Higher-order corrections improve the approximation towards the exact energies.

The method explains the good agreement of approximate theories with numerical spectra.

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.