Continuity conditions for a time-dependent wavefunction

In addition to the usual condition of continuity of the wavefunction and of its derivative with respect to position, continuity with respect to time i s necessary in a solution of the time-dependent Schrodinger equation. For a particle interacting with an oscillatory field, two different procedures t o ensure this continuity are presented and tested. These methods are effici ent to calculate the probabilities for absorption or emission of photons by a particle incident on a potential of arbitrary shape, even in intense fie ld situations. We apply the formalism to an examination of a criterion give n by Buttiker and Landauer to define the time it tal;es for a particle to t unnel through a barrier. (C) 1999 Elsevier Science B.V. All rights reserved .