At t=0, a particle in an infinite square well of width L is found in a linear combination of two stationary states of energies E2 and E3 :
Ψ(x,t)=A(ψ2(x)+2ψ3(x))
a) Find A by normalizing Ψ(x,t=0). Don't forget to make use of the fact that the stationary states are orthonormal
b) Find Ψ(x,t) and ∣Ψ(x,t)∣². Express the latter as a sinusoidal function of time
c) Check whether Ψ(x,t) is normalized