for each of the following one-dimensional cases, verify that the given wavefunction satisfies the Schrodinger equation, and derive an expression...

for each of the following one-dimensional cases, verify that the given wavefunction satisfies the Schrodinger equation, and derive an expression for the energy of the system:
a) psi= sqrt(2/L)sin(3pix/L), V=0
b) psi= Ae^(-ikx) + Be^(-iKx), V=constant