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## Homework Statement

Find the eigenfunctions of a particle in a infinite well and express the position operator in the basis of said functions.

## Homework Equations

## The Attempt at a Solution

Tell me if I'm right so far (the |E> are the eigenkets)

[itex]X_{ij}= \langle E_i \vert \hat{X} \vert E_j \rangle = \int dx \int dx' \langle E_i \vert x \rangle \langle x \vert \hat{X} \vert x'\rangle \langle x'\vert E_j \rangle [/itex]

[itex] \int dx \int dx' \Psi_i^*(x) x\delta_{x, x'} \Psi_j(x') = \int dx \Psi_i^*(x) x \Psi_j(x) [/itex]

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