Coulomb-diamagnetic problem in two dimensions

Abstract

Based on a conjecture for the four-step recursion relation occurring in the series solution of the Coulomb-diamagnetic problem in two space dimensions, the energy eigenvalue spectrum that reproduces the known limits in full is obtained exactly. The resulting nonperturbative spectrum is a deceptively simple combination of the purely Landau and Coulombic spectra but gives the quasi-Landau levels with (3/2)ħωc spacing near the ionization threshold. The conjecture is made plausible in terms of an adiabatic continuation of solutions in the parameter ratio ħωc/scrR.