Compression effects on dipole transitions and state lifetimes for a hydrogen atom

Abstract

The quantum mechanical problem of a hydrogen atom placed at the center of an impenetrable sphere of radius r0 is solved by using two different methods, where, in the first, a trial wave function, consisting of a hydrogen-like function times a cutoff factor that ensures fulfillment of Dirichlet boundary condition, is proposed, whereas in the second, the radial Schrödinger equation is solved by means of an accurate numerical technique. We computed the energies for the ground and first excited states of S-, P-, and D-symmetry, as well as dipole transitions, oscillator strengths, and a few state lifetimes. Although the variational method and the numerical solution are found to give similar qualitative behaviours, which, in general, compare reasonably well with some results published previously, the 2p state lifetimes obtained in the present calculations appear to be at variance with the latter at some particular box radii.