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carllacan
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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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