Rigorous analytical lower bound on the ground-state energies of hydrogenic atoms in high magnetic fields

Abstract

By employing the virial theorem and Hellmann-Feynman relation in combination with the pertinent uncertainty-principle inequality, one can derive a rigorous lower bound on the ground- state energies of hydrogenic atoms in magnetic fields of arbitrarily large intensity, ${E}_{0}$>\ensuremath{\lambda}(3t-${t}^{\mathrm{\ensuremath{-}}1}$-2.00232) Ry, where the magnetic field enters through the parameter \ensuremath{\lambda}\ensuremath{\equiv}B/(4.701\ifmmode\times\else\texttimes\fi{}${10}^{9}$ G) and t is defined implicitly by t(1-${t}^{2}$${)}^{\mathrm{\ensuremath{-}}2}$=\ensuremath{\lambda}${Z}^{\mathrm{\ensuremath{-}}2}$ for atomic number Z. With straightforward modifications, the method presented here can also be employed to derive rigorous analytical lower bounds on the ground-state energies of other parameter-dependent nonseparable quantum systems.