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## Homework Statement

Hi all.

At time t<0 a particle is in the stationary state [itex]\left| {\psi _0 } \right\rangle [/itex] of the harmonic oscillator with frequency omega

_{1}(i.e. the ground state of the H.O.).

At t=0 the Hamiltonian changes in such a way that the new angular frequency is omega = omega

_{1}/2. We assume that at t=0 the particle is

**still**in the state [itex]\left| {\psi _0 } \right\rangle [/itex], but for t>0 the state evolves according to the new Hamiltonian with omega = omega

_{1}/2.

I wish to find the expectation value of position, x, for all times t.

## The Attempt at a Solution

For t<0 it is easy, since the particle is in the stationary state, so using raising/lowering operators, one findes that <x> = 0 for t<0.

For t>0 I don't think it is so trivial, since the particle is now in a superposition of all the possible states. If I use raising/lowering operators to find <x> for t>0, I get an infinite sum (of course it might converge, but still ..).

Do you have any suggestions for the case t>0?

Best regards,

Niles.