Changing potential in harmonic oscillator

[facetten]

i have a quick question
A particle in ground state of a S.H.O whose potential is given by

$$V_1(X)=\frac{1}{2}mw^2_1x^2$$
suddenly changes to

$$V_2(X)=\frac{1}{2}mw^2_2(x-x_o)^2$$

what is the wavefunction going to be like for the new potential?

i'd think everything else stays the same in the wavefunction except replacing x with (x-x_o) and

w_1 with w_2?

 

[Amok]

If the change is really sudden, then immediately after the change the wavefunction is going to be exactly the same as before. If you let the system evolve, then it will change to "adapt" to V2, according to the TDSE with the initial conditions being that the wavefunction at t=0 will be equal to the wavefunction corresponding to the initial potential. A process that changes very rapidly is called a diabatic process.