i have met a problem about the commutator of x and p. [x,p]=ihbar /p> is the eigenstate of momentum operator p. <p/xp-px/p> =<p/xp/p>-<p/px/p> =p<p/x/p>-p<p/x/p> the second term is got by the momentum operator p acting on the left state. =0 so i get zero! is there anyone can point out where i am wrong?
Can you calculate <p|x|p>? Which number will you get? I can tell you: any number you want, depending on how you decide to calculate it. You are playing pseudo-math with formal expressions without really understanding their mathematical meaning. That is how many paradoxes appear. Many theorems in mathematics are valid under certain assumptions. Skip the assumptions, apply the theorem, and you can well create a paradox.
Take a look at Post #18 in this (very recent) thread: https://www.physicsforums.com/showthread.php?t=426509&page=2 More importantly, check out the references I mentioned. :-)