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

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, $E_0$>λ(3t-$t^{\mathrm{-}1}$-2.00232) Ry, where the magnetic field enters through the parameter λ≡B/(4.701×${10}^9$ G) and t is defined implicitly by t(1-$t^2$ ${)}^{\mathrm{-}2}$=λ$Z^{\mathrm{-}2}$ 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.