I am not really asking how to solve the problem but just for explanation of what I know to be true from the problems solution. Basically the original problem statement is this: A particle in a harmonic oscillator potential starts out in the state |psi(x,0)>=1/5 * [3|0> + 4|1>] and it asks to find the expectation value of position <x>. Now the way I approached the problem was to first find |psi(x,t)> by simply "tacking on" the time dependent exponential terms and then expressing x through the ladder operators a+ and a-. What I am wondering is when I, for example, apply the raising operator a+ to the state |0>*exp(-i*E0*t/h) does the function become |1>*exp(-i*E0*t/h) rather than |1>*exp(-i*E1*t/h) (i.e. why does the energy term in the time dependent part not change?) Thanks!