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a) A free particle of mass m moves in one-dimensional space in the interval 0 <= x, with enery E. There is a rigid wall at x = 0. Write down a time-independent wavefunction, which satisfies these conditions, in term of x and k wher k is the wave vector of the motion. State the relation between k and E for this wavefunction.

b) Show explicity that the wavefunction you have found in part a) is an eigenfunction of the Hamitonian for this system.

c) What is the time-dependent state, psi(x,t). corresponding to the wavefunction psi(x)?