The solutions to the (linear and nonlinear) Schrodinger equations become oscillatory when the Planck constant is small, in the so-called semiclassical regime. Numerically one often has to resolve the small Planck constant in order to obtain the physically correct solutions. We prove an optimal mesh strategy for a time splitting spectral method for the linear Schrodinger equation, and show similar strategy for nonlinear Schrodinger equations. In the linear case, we also derive multiphase equations for the semiclassical limit using the Wigner transformation and kinetic moment closure, and derive a kinetic scheme for the multiphase equations capable of capturing finite number of phases.