Time dependence of Lippmann-Schwinger states

Abstract

Due to the presence of an infinitesimal parameter ε in the resolvent, the Lippmann-Schwinger states cannot be strict eigenstates of the Hamiltonian, and their time evolution is very non-trivial (in agreement with Fermi's golden rule). In sharp contrast, strict Schrödinger eigenstates cannot make transitions into free channels. Artefacts such as adiabatic switching, wave packets, or infinite time span are not needed in our analysis.