Generalized space translation and new numerical methods for time-dependentSchroedinger equations of molecules in intense laser fields

We present new numerical methods, based on a Generalized Space Translation representation (GST), for solving the Time-Dependent Schroedinger equation (TDSE), to treat the nonlinear, nonperturbative interaction of molecules wi th intense laser pulses. Adopting a Lagrangian, moving coordinate system, w e generalize the previous Space Translation method (ST), used in atom-laser interaction problem. In this representation (gauge), the reference system is moving with the laser pulse so the classical movement of free particles in the field, i.e. in the asymptotic region where electron-molecule potenti als,are negligible but the laser field is still present, is exactly describ ed. As a consequence, the asymptotic quantum wave functions are exact in pr esence of the laser pulse. To solve numerically the GST-TDSE, all standard discrete propagators for the time discretization and all efficient space di scretization methods can be applied. In order to illustrate different possi bilities for the choice of discretization methods, we have tested several t ypes of split-operator (SO) and alternating direction implicit (ADI) method s combined with adaptive finite difference methods for the 3D Born-Oppenhei mer simulation of H-2(+) in a short intense laser pulse field. Our comparis on of convergence between the same discretization methods for different gau ges have demonstrated the superiority of the GST method. As examples, we pr esent for the first time the ionization of H-2(+) exposed to a circularly o r linearly polarized intense laser pulse perpendicular to the internuclear axis by an exact 3D simulation. (C) 2001 Elsevier Science B.V. All rights r eserved.