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This paper deals with exact formulas for the resolvent kernels and exactsolutions of time dependent Schr\"odinger equations under a uniform magneticfield on the hyperbolic half plane $\H$, and under a diatomic molecular Morsepotential on the real line $\R$.

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 $\