Consider a particle of mass m trapped in an infinite well of width L. It has an initial wavefunction (x, 0) = sin(x/L)

Consider a particle of mass m trapped in an infinite well of width L. It has an initial wavefunction ψ(x, 0) = α sin(πx/L) β sin(2πx/L), where α and β are complex constants. 

Answer the following questions. 

(a) Comment on the possible values of α and β. 

(b) Find the time-dependent wavefunction. 

(c) Compute the expected momentum and position as a function of time.