Radiation conditions for the time-dependent Schrödinger equation: Application to strong-field photoionization

Abstract

Radiation conditions are introduced as an exact method to truncate numerical solutions of the timedependent Schrödinger-equation at the boundaries of the numerical grid. A rigorous derivation of radiation conditions is given by the Green-function method for one-and three-dimensional regions. An accurate finitedifference representation is obtained for a one-dimensional region. The method is applied to calculations of strong-field photoionization. The calculation of ionization probabilities and energy spectra by the truncated solution is illustrated. ͓S1050-2947͑97͒06107-6͔PACS number͑s͒: 32.80.Rm, 31.15.Ϫp

Numerical calculation of strong-field laser-atom interaction: An approach with perfect reflection-free radiation boundary conditions

“…The present 3D-problem differs from the 1D-problem, treated previously in [18], by the presence of the effective potential l(l + 1)/(2r 2 ). We will recover the 1D result in the special case l = 0 and in the limiting case R → ∞ later in this section.…”

“…The first, l-independent part of (12) is the Green's function of a 1D half-space, which was already derived in [18]. This 1D result is contained in (12) in the special case l = 0, since κ (0) 1 = 0.…”

“…Following the Green's function formalism [18,22], the solution of (4) at any coordinate r ≥ R and time t ≥ 0 can be calculated as…”

“…Nonlocal boundary conditions have already been successfully used in a number of 1D calculations [18][19][20][21], however, the generalization to three dimensions and the inclusion of the laser interaction, lacking spherical symmetry, requires substantial modifications. In a first step, the present boundary conditions have been generalized from 1D to 3D without laser field [22].…”

Hybrid surface-flux method for extraction of the ionization amplitude from the calculated wave function

“…For this purpose in the capacity of a model system we used the one-dimensional system [4,7] i ∂ψ(x, t) ∂t = − 1 2…”