Siegert-state expansion for nonstationary systems: Coupled equations in the one-channel case

Abstract

Expansion of the solution to the time-dependent Schr\odinger equation for a one-channel nonstationary system in terms of Siegert states is discussed. A discrete set of coupled pseudodifferential equations defining time evolution of the coefficients in the expansion is derived, and physical observables (probabilities of transitions to discrete states and the spectrum of ejected particles) are expressed in terms of these coefficients. In contrast to other time-dependent close-coupling methods in atomic and molecular physics, the present approach treats the continuum with no approximation. A price for that is a more involved mathematical structure of the resulting coupled equations. The approach is implemented in terms of Siegert pseudostates and illustrated by calculations for a model time-dependent rectangular potential.