My lecturer made a statement: In the infinite square well potential $x\psi_n(x)$ (where $\psi_n$ is just the spatial part of an energy eigenstate) can be expressed as a linear combination of the energy eigenstates of the infinite square well, i.e. $x\psi_n(x) = \sum > c_m\psi_m(x)$. This came about by applying the position operator on an arbitrary wavefunction.
I can't see how this function is a linear combination of the energy eigenstates.
Thanks
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