1. The problem statement, all variables and given/known data Hi all, i have a problem: i am given a time-dependent wavefunction, Ψ(x,t), and i am asked to calculate the expectation value of total energy E(t) and potential energy V(t). Ψ(x,t) = (1/sqrt2)[Ψ0(x).e-[i(E0)t/h] + Ψ1(x)e-[i(E1)t/h]], where Ψ0,1(x) are the ground and first excited normalised eigenstate of the linear harmonic oscillator, n=0,1. What i have tried is <E(t)> ∫Ψ*(x,t).E^.Ψ(x,t) dx, where E^ is E(hat), the total energy operator (the hamiltonian?). the integrals are between x = minus and plus infinity by the way. i have been through a hell of a lot of integration (2 sides of small handwriting) and came up with an answer i am not happy with. So, my first query is, am i using the correct energy operator, E^ = -(h2/2m).(d2/dx2) + V(x), or is it something else? the reason i ask this is because i just lifted it straight from the time-independent schrodinger equation, but my Ψ(x,t) is clearly time-dependent, so does this change the operator i need? also, i have done the same thing for the potential with V^ = V(x), but i did not know what i was supposed to do with V(x) when it came to applying it to Ψ(x,t) to the right of it. So, i just called it V(x) and got on with it. After this was worked out my answer was <E(t)> ∫Ψ*(x,t).V.Ψ(x,t) dx = V. So my second query is, for a linear harmonic oscillator, is there something more specific i am meant use than just V^ = V(x) = V ?? other than that, am i approaching this problem all wrong or what? i'm quite new to quantum mechanics so i'm never really sure if my solutions even resemble the actual answer. i don't even feel as if i've asked these questions very well. Thanks. PS. just incase, time-independent schrodinger equation: [-(h2/2m).(d2/dx2) + V(x)]Ψ(x) = EΨ(x) time-dependent schrodinger equation: Ψ(x,t) = Ψ(x)e-iEt/h the other thing was there was something in my notes about <E> that says <E> = (∑n) |an|2En that i thought might be useful here but i really dont get how to use it - if anyone could explain to me about that, if it is relevant, i'd really appreciate it. Thanks.