Calculation of high-frequency spectral wings by solution of the Schrödinger equation in the complex plane

Abstract

We discuss a method of overcoming the large-phase-cancellation problem, due to rapid oscillations of the integrand, which arises when trying to compute far off-diagonal radiative matrix elements, relevant for spectral wings. The method involves (a) distorting the matrix-element integration path from the real axis to a contour in the complex plane, and (b) solving the Schrödinger equation exactly (numerically) along the contour. The contour is chosen to eliminate, or reduce greatly, the oscillations in the integrand for the matrix element.