Half-Harmonic Oscillator to Full-Harmonic Potential

[Eigengore]

Homework Statement

This problem was already answered:
"I have to find the allowed energies of this potential:

V(x)= (mω2^2)/2 for x>0
infinite for x<0

My suggestion is that all the odd-numbered energies (n = 1, 3, 5...) in the ordinary harmonic osc. potential are allowed since
ψ(0)=0
in the corresponding wave functions and this is consistent with the fact that
ψ(x)
has to be 0 where the potential is infinite."

now the new inquiry is that if the infinite potential is removed instantly. What is the probability of maintaining the same energy.

Homework Equations

none given aside from the other post

The Attempt at a Solution

my guess is that it shouldn't change because the odd solution is already part of the new solutions, thus it shouldn't switch. But I am tempted to consider that there are twofold more states to go to so the probability of maintaining the state is 0.5

 

[vela]

Instead of guessing, why don't you calculate the probability?