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, E₀>{λ}(3t-t^-1-2.00232) Ry, where the magnetic field enters through the parameter {λ}{≡}B/(4.701×{}10⁹ G) and t is defined implicitly by t(1-t²{)}^{{{-}}2}=λ{Z}^{{{-}}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.