How Does Changing the Spring Constant Affect Quantum State Probabilities?

[sutupidmath]

Homework Statement

A particle is in the ground state of the harmonic oscillator with classical frequency w, when suddenly the spring constant quadruples, so w'=2w, without initially changing the wave function. What is the probability that a measurement of the energy would still return the value hw/2? What is the probability of getting hw?

Homework Equations

The Attempt at a Solution

I know that |c_n|^2 tell us the probability that a measurement will give energy E_n. But in this case i kind of don't know where to start.

So, if you could give me some direction, i would appreciate it.

 

[vela]

You know the particle is in the ground state of the original Hamiltonian immediately after the spring constant changes. This state, however, is no longer an eigenstate of the new Hamiltonian, so you want to do is find the overlap of the particle's state with the relevant new eigenstates.