Assuming the eigenvalue of position operator x equal to k, can I not write

<PSIn|x|PSIm>=<xPSIn|PSIm> =<kPSIn|PSIm> =k<PSIn|PSIm> =kDELTAnm But I know that =0 in case of even potentials(I don't know how that happens ) and what I have written above is wrong , at least in case of even potentials. Please help!