The Propagators for δ and δ′ Potentials With Time-Dependent Strengths

Abstract

We study the time-dependent Schrödinger equation with finite number of Dirac δ and δ′ potentials with time dependent strengths in one dimension. We obtain the formal solution for generic time dependent strengths and then we study the particular cases for single delta potential and limiting cases for finitely many delta potentials. Finally, we investigate the solution of time dependent Schrödinger equation for δ′ potential with particular forms of the strengths.