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Homework Statement
I posted a picture of the question https://imgur.com/a/8byywYL
Homework Equations
P = $$(<\psi_{n}\psi_{o}>)^2$$
The Attempt at a Solution
I am guessing that I compute(denote by ##\psi_{o}## the ground state of the old well and by ##\psi_{n}## the ground state of the new well) $$(<\psi_{n}\psi_{o}>)^2$$ I think this answer is meaningless because the system itself changed. The well is no longer the same. How can we take a state of one system and take its inner product with a state from a completely different system? I have a feeling that the answer to the first part of the question is zero, because in the question it is said "the wave function does not change". I do not understand how the artificial nature of this question can give any meaningful answer.
Maybe since the question does not specify a certain point in time, the answer is the same for all times, and is thus thatfor initial time.
Also, the state is stationary if it is an energy eigenvector, but how can we know if it is one?
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