A sudden change in the depth of delta function potential well

[Mazhar12]

Homework Statement

If a particle is initially in the bound state of a delta function potential well, having depth A, and at some point in time the depth suddenly changes to B. What is the probability that the particle will now be in the states of the continuum spectrum? both A and B are greater than zero.

Relevant Equations

equations are attached.

is it correct that the continuum states will be free particle states? and the probability will be |< Ψf | ΨB>|^2 . Where Ψf is the wave function for free particle and ΨB is the wave function for the bound state when the depth is B.

 

[anuttarasammyak]

Because we are well aware of the old and new bound states $|BS_A>$ and $|BS_B>$, we can calculate
$$1-|<BS_A|BS_B>|^2$$
and I assume it as probability of transfer to unbound states.
I wonder it says relative magnitude of A and B, so deepening or shallowing of well, does not matter. Maybe I am wrong.