Class of invariants for a time dependent linear potential

Abstract

General solution of the one-dimensional Schrodinger equation in presence of a time-dependent linear potential is reconsidered in the context of Lewis–Riesenfeld and unitary transformation approaches. Three invariant operators are constructed as limiting cases of a general Hermitian quadratic invariant and their instantaneous eigenfunctions are obtained. Then the corresponding solutions of Schrodinger equation for each invariant operator are derived. These solutions include all known solutions of the system. Furthermore, it is shown how different solutions can be related to each other.