Principles of Limiting Absorption and Limiting Amplitude in Scattering Theory. I. Schrödinger's Equation

Abstract

The outgoing solution of the time‐independent Schrödinger equation, with a suitably restricted real potential, is shown to be the uniform limit of the square‐integrable solutions of the same equation with complex energy as the imaginary part of the energy tends to zero. Under further restrictions on the potential, it is also shown that the solution to the initial‐value problem for the time‐dependent Schrödinger equation tends to the outgoing solution as time increases indefinitely.