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- Homework Statement
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- Relevant Equations
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My approach was: $$\psi_{2g} = \sqrt{1/L}sin(\frac{n \pi x}{2L}) = \sum c_n \sqrt {\frac{2}{L}} sin(\frac{n \pi x}{L})$$A particle is in the ground state of a box of length L. Suddenly the box

expands (symmetrically) to twice its size, leaving the wave function undisturbed. Show that

the probability of finding the particle in the ground state of the new box is ##(8/З\pi)^2.##

Summarizing what i have done after that (Fourier series and sum of infinite series), we get the result realizing that, what we want matematically is ##P## $$P = \frac{(c_1)^2}{\sum_{n=1}^{n=\infty} (c_n)^2}$$

The main thing that bothers me is the necessity to calculate the infinite series. It is possible, indeed, even if we use wolframalpha https://www.wolframalpha.com/input?i=\sum+of+(n^2/(1-4n^2)^2)+from+1+to+infinity

BUT, i could not use it on a test, neither would have time to do that. So even so i have got the right answer, i want to know if there is a better approach to this problem.

Thank you