1. The problem statement, all variables and given/known data The expectation value of motion of a particle over a time interval t-to is C(t,to) = <0|x(t)x(to)|0> (product of position operators in Heisenberg representation for ground state harmonic oscillator) 2. Relevant equations Schrodinger picture: <ψ(t)|Ω|ψ(t)> = <ψ(to)|U+(t,to) Ω U(t,to)|ψ(to)> I believe: U(t,to) = exp[-iωt/h] U+(t,to) = exp[iωt/h] Heisenberg rep: time-indep states, time-dep operators Schrodinger rep: time-dep states, time-indep operators 3. The attempt at a solution I'm confused about how to convert x(t) in the Heisenberg representation to the Schrodinger representation and how to incorporate it into C(t,to). Here is what I scribbled: <x(t)> = <ψ(t)|x(to)|ψ(t)> = <ψ(to)|exp[iωt/h] x(to) exp[-iωt/h]|ψ(to)> = <0|exp[iωt/h] x(to) exp[-iωt/h]|0> Is the first equality even true? The question seems like it should be simple, but I am sincerely confused. Thanks for your time and for any help!