This might be trivial for some people but this has been bothering lately. If P is momentum operator and p its eigenvalue then the eigenfunction is up(x) = exp(ipx/h). where h is the reduced Planck constant (sorry cant find a way to make the proper notation). While it can also be proved that <x|p> = exp(ipx/h) (omitting constant pre factor), where |p> is also momentum operator eigenfunction in different notation, in this sense one would say that up(x) = |p>. But why is <x|p> = up(x) instead? I will appreciate anyone who is trying to enlighten me in this problem. Thanks in advance.