The Cauchy Problem for Schrödinger Equations with Time-Dependent Hamiltonian

Abstract

We consider the Cauchy problem for a Schrödinger equation with an Hamiltonian depending also on the time variable and that may vanish at t = 0. We find optimal Levi conditions for well-posedness in Sobolev and Gevrey spaces.

Keywords

• Degenerate Schrödinger equations
• Cauchy problem
• necessity of Levi conditions
• Gevrey well-posedness