N-dimensional electron in an anharmonic potential: The large-N limit

We show that the energy levels predicted by a 1N-expansion method for an N-dimensional electron in an anharmonic potential are always lower than the exact energy levels but monotonically converge toward 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 with numerical results.