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jyoung11509

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## Homework Statement

Assume a potential of the form [tex]V(x)=V_{0}sin({\frac{\pi x}{L}})[/tex] with 0<x<L and [tex]V(x)=\infty[/tex] outside this range. Assume [tex]\psi = \sum a_{j} \phi_{j}(x)[/tex], where [tex]\phi_{j}(x)[/tex] are solutions for the infinite square well. Construct the ground state wavefunction using at least 10 basis functions.

## Homework Equations

I obtained the solution [tex]\phi_{n} = \sqrt{\frac{2}{L}} \sin({\frac{n\pi x}{L}})[/tex] for the infinite square well with zero potential inside.

## The Attempt at a Solution

After obtaining the solution shown above, I attempted to expand the summation. I know that I want to do a linear combination of energy eigenstates, however, I am not sure what to do about the leading coefficients. I have found by searching that [tex]a_{j} = \int_{-\infty}^{\infty} \phi_{j}^{*}(x) \psi dx[/tex], but how can I solve this if I'm using the [tex]a_{j}[/tex]'s to find [tex]\psi[/tex]?

Any help or advice would be greatly appreciated. Thanks!