To deduce the momentum representation of $[x,p]$, we can see one paradom
$$<p|[x,p]|p>=iā$$
$$<p|[x,p]|p>=<p|xp|p>ā<p|px|p>=p<p|x|p>āp<p|x|p>=0$$
Why? If we deduce the momentum representation of $x$, we obtain $<p|x|p>=i\hbar \frac{\partial \delta (p'-p)}{\partial p'}|_{p'=p}$. This value is not definite. So, why two uncertain values can obtained a certain value $i\hbar$? In addition, the $x$ should be replace by $i\hbar \frac{\partial }{\partial p}$. Then the eigenvalue p can't extract. However, if we consider $i\hbar \frac{\partial }{\partial p}$ to act on the bra, not the ket, then the eigenvalue p can be extracted. Is anything wrong here?
