Doubling the frequency of a quantum harmonic oscillator

[Cadenzie]

Homework Statement

A particle is in the ground state of a harmonic oscillator with classical frequency w. Suddenly the classical frequency doubles, w -> w' = 2w without initially changing the wavefunction. Instantaneously afterwards, what is the probability that a measurement of energy would still return the value h'w/2? (where h' denotes h-bar).

Homework Equations

Earlier in the question, I had to show that H = (a'*a + 1/2)h'w where a' and a are the creating and annihilation operators, respectively. Also, En = (n+1/2)h'w for a harmonic oscillator.

The Attempt at a Solution

I'm honestly not at all sure how to approach this; my instinct would be to say that it has a probability of 0, but that seems unlikely.

 

[member 553083]

I know that the wavefunction is psi_n = (1/sqrt(2^n * n!))*(a'^n)*psi_0, so a measurement of energy after the frequency has changed would be En' = (n+1/2)h'w' = (n+1/2)(2)h'w. Any help would be greatly appreciated; thank you!