Resolvent kernels and time dependent Schr\" odinger equations under magnetic field on the hyperbolic half plane \H and the Morse potential on the real line $\

This paper deals with exact formulas for the resolvent kernels and exact solutions of time dependent Schr"odinger equations under a uniform magnetic field on the hyperbolic half plane \H, and under a diatomic molecular Morse potential on the real line $\mathbb{R}$.