Expectation Value of Energy for Nonstationary State in Infinite Square Well

[KHU2]

8)
Consider a particle in an infinite square well of width L. Initially, (at t=0) the system is
described by a wavefunction that is equal parts a superposition of the ground and first
excited states:
Ψ(x, 0)=C[Ψ1(x)+Ψ2(x)]
a) Find C so that the wavefunction is normalized
b) Find the wave function at any later time t.
c)show that the expectation value of the energy in this state is (E1+E2)/2, where E1 AND E2 ARE THE ENERGIES OF THE FIRST TWO STATIONARY STATES.


I DID a) and b) , i don't how to do c) , could you help me

 

[siddharth]

So, if $$\psi(x,t)$$ is your wavefunction, what is the expectation value of the Hamiltonian operator?

 

[olgranpappy]

p.s. you may just do it at t=0, but don't forget to prove that you *can*.