Abstract

The time-dependent Schrodinger for an atom in a radiation field has a very special form, at least within the dipole approximation: The time-dependence of the Hamiltonian is contained entirely in a c-number which appears as a factor in the interaction, V(t), of the atom with the radiation field. In the velocity gauge this factor is the vector potential, A(t), of the field — we have V(t)= − (e/µc)A (t) • p, where e, µ, and p are the charge, reduced mass, and canonical momentum (in the center of mass frame) of the electron — while in the length gauge this factor is the electric field vector F(t) — we have V(t) = –eF(t) • x, where x is the position coordinate. To our knowledge, this factorization property has not been fully exploited in previous approaches to solving the timedependent Schrodinger equation¹. As we show here, in an application to multiphoton ionization of atomic hydrogen, it is an extremely useful property; and although at first sight it would seem to be a unique feature of the atom-radiation system, this is not so, for, as Solov’ev² has pointed out, the time-dependent Schrödinger equation for colliding atoms or ions can be transformed into a form in which a scaled time-dependence also appears only in c-number factors of the (transformed) interactions.

© 1991 Optical Society of America