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One dimensional infinite square, particle with mass

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1- Consider a particle with mass m in the one dimensional infinite square ell potential V(x) with length L at time t=0, the wave function for this particle psi (x) =A sin(pi x/L) cos(pi x/L)

a) find the coefficient A so that the wave function is properly normalized.
b) what is the probability of finding particle between 0<x< L/2?
c) what is the probability of finding ground state at later time t>0?

2- Consider an electron of mass m= 0.9x10^-30 kg in a infinite box of dimension L= 10^-9 m. What is the energy different between the ground state and first excited state?(Express your answer in eV).

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The expert examines one dimensional infinite squares for particles with a mass.