particle on a ring, quantum mechanics

Question

A)Explain the reason why Ψ(x) = Acos(πx/L) is not able to describe a particle of mass m in a ring of length L.

B) On the other hand, explain why Ψ(x) = Acos^2(πx/L) is.

C) When momentum is measured, what values can be obtained and with what probabilities? (relative and absolute).

(D) Normalize Ψ(x) so the probabilities add up to 1

(E)Taking this Ψ(x) as the initial state of the system, Ψ(x,0). find the state of the system after a time t, Ψ(x,t)

Answer 1

a) doesn't satisfy boundary condition Ψ(0)=Ψ(L)

b) does