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Trace of Position and Momentum Operator

  1. Sep 5, 2013 #1
    1. The problem statement, all variables and given/known data

    Hi guys, I've not started a course on QM yet, but we are currently learning the maths used in QM.


    Show, by taking the trace of both sides show that finite dimensional matrix representations
    of the momentum operator p and the position operator x which satisfy [p, x] = −ih are not possible.

    Why does this argument fail if the matrices are infinite-dimensional (as Heisenberg’s were)?

    15plh50.png

    2. Relevant equations



    3. The attempt at a solution

    Are the position and momentum operators supposed to be matrices? I've looked up on wikipedia, the position operator is more of like ih(d/dp) while the momentum operator is ih(d/dx).
     
    Last edited: Sep 5, 2013
  2. jcsd
  3. Sep 5, 2013 #2
    I believe this link will help you understand.

    http://www.asianscientist.com/books/wp-content/uploads/2013/05/7271_chap02.pdf [Broken]
     
    Last edited by a moderator: May 6, 2017
  4. Sep 6, 2013 #3
    It looks difficult but I will give it a go.
     
    Last edited by a moderator: May 6, 2017
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