# Infinite square well potential suddenly moved

A ptl is initially in its ground state in a box with infinite walls at x=0 and a. The wall of the box at x=a is suddenly moved to 2a.
(Energy conserved, wave fn. remains the same, basis changed)
We can calculate the probability that the ptl will be found in the ground state of the expanded box expanding initial wave fn with new basis(k= 2aPi/n )..

But..how can we find the state of the expanded box most likely to be occupied by the ptl?(By the same method?? Calculate general expression of coefficent c_n=<ψ_n|ψ_1> and find n such that |c_n|^2 max? it seems hard to find n)

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Have you already calculated the coefficients c_n? There isn't any other obvious method of finding the n for which |c_n|^2 is maximum, except than actually solving the function n->c_n, and then trying to find the maximum.

I have no idea what kind of function it is going to be, but one should check if the extension to real variables x->c(x) has the zero point of the derivative easily solvable. Then the n and n+1 for which n<x0<n+1 are only possibilities for the maximum.

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sorry..I did some computation, got |c_1|=4*2^1/2/3Pi, |c_2|=2^1/2/2 and the others less than them..

so the system is most likely to be occupied by |ψ_2> whose energy is E2`(=E1) as expected..

thx..