Uniqueness of solutions to Schrödinger equations on complex semi-simple Lie groups (Q2457829)

The author considers the time-dependent Schrödinger equation on complex semi-simple Lie groups. It is shown that if the initial data is a bi-invariant function that has sufficient decay and the solution has sufficient decay at another fixed value of time, then the solution has to be identically zero for all time. Strichartz and decay estimates for the Schrödinger equation are also derived. On the Heisenberg group the failure to obtain a parametrix for the Schrödinger equation is related to the fact that geodesics project to circles on the contact plane at the identity.