To deduce the momentum representation of ##[x,p]##, we can see one paradom(adsbygoogle = window.adsbygoogle || []).push({});

##<p|[x,p]|p>=i\hbar##

##<p|[x,p]|p>=<p|xp|p>-<p|px|p>=p<p|x|p>-p<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?

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# The momentum representation of ##x## and ##[x,p]##

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