ENERGY SHIFTS OF BOUND-STATES IN STRONG RADIATION-FIELDS

By applying a Lie-algebra method [Phys. Rev. A 42, 4302 (1990); 47, 5213(E) (1993)], we obtain analytical solutions and energy eigenvalues for a charged harmonic oscillator interacting with a single-mode photon field. The energy shifts of bound states of the harmonic oscillator due to the radiation field is also derived. By a variational method, we show that any bound state in a central potential which satisfies a power law can be treated as a harmonic oscillator around its average radial position. With this idea, we generalize the energy-shift formula obtained for a harmonic oscillator to the hydrogen-atom case. Our result shows that the energy shifts depend on the principal quantum number according to an inverse-square law.