1. The problem statement, all variables and given/known data We are considering the Superposition state: ψ(x,t) = 1/2 u1(x)e(-i/hbar)E1t + √3/2 u4(x) e(-i/hbar)E4t We had to verify that ψ is a solution of the time dependent Schrodinger Equation, which I have done. Next we are asked to show that ψ is NOT an energy eigenfunction and therefore not a solution to the time independent Schrodinger Equation. 2. Relevant equations Time Independent Schrodinger Equation: H(ψ(x,t)) = Enψ(x,t) Hamiltonian operator: H= (-hbar/2m)∇2+V(x) 3. The attempt at a solution At first I tried to see if I could somehow show that the first equation did not hold and tried to apply the Hamiltonian on the left hand side, but I was just left with ∇2u(x) terms and I couldn't think of any way of simplifying them. Then I considered the time dependent Schrodinger which states that the Hamiltonian of ψ is equal to (i*hbar)dψ/dt. So I then set the right hand sides of each Schr. equation equal to each other (as the left hand side of both is the Hamiltonian) and tried to go about showing that this equality did not hold. I can't seem to get anywhere with this method. I'm wondering if there's a simpler way of doing this?