Particle in a box

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Statement
A particle of mass m is confined to move in a box of length L. The potential energy of the particle within the box is zero and rises abruptly to a very large value (i.e. infinity) at the walls of the box. The walls of the box are now pulled out so that the box has length 2L. The walls are pulled out sufficiently quickly that instantaneously the state of the particle doesn’t change. The position of the particle is now measured and the outcome is that the particle is located exactly at the centre of the box (i.e. it is represented by a Dirac delta function located in the middle of the box). The energy of the particle is again measured.

Question
What is the probability that the outcome of this measurement will be the ground state energy? the first excited state?

My input
It actually contained more questions, but the last 2 are the ones i require help in. anyone with any idea? im not too knowledgeable about dirac delta functions. im not sure how i can get schrodinger's equation into something that can measure the probability of the ground state or 1st excited state.
 
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Answers and Replies

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Hootenanny
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Welcome to Physics Forums.

HINT: Can you write the wave function of the second potential (box of width 2L) in terms of the energy eigenfunctions of the initial potential (box of with L)?
 

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