Unique continuation for the Schrödinger equation with gradient term

Abstract

We obtain a unique continuation result for the differential inequality vertical bar(i partial derivative(t) + Delta)u vertical bar <= vertical bar Vu vertical bar + vertical bar W . del u vertical bar by establishing L-2 Carleman estimates. Here, V is a scalar function and W is a vector function, which may be time-dependent or time-independent. As a consequence, we give a similar result for the magnetic Schrodinger equation.