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Canonical commutation relations

  1. Mar 6, 2015 #1
    Hi ,

    I need help with the this exercise:

    a) Work out all of the canonical commutation relations for components of the operators r and p:
    [x,y]
    [x,py]
    [x,px]
    [py,pz]
    and so on. Answer:
    [ri,pj]=−[pi,rj]=iℏδij
    [ri,rj]=−[pi,pj]=0
    , where the indices stand for x, y, or z and
    rx=x
    ry=y
    rz=z
    where
    p^=−iℏ∂∂x


    Formula: [A,B]=AB-BA

    Can someone give a hint?

    Thanks!
     
  2. jcsd
  3. Mar 6, 2015 #2

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Hello Armani II, welcome to PF :smile: !

    Somehow the template was lost, hopefully by accident. Its use is mandatory in PF, for good reasons (##\leftarrow\ ##click to see the guidelines).

    1. The problem statement, all variables and given/known data
    2. Relevant equations
    3. The attempt at a solution

    What is your attempt ? Ever look at something like ## x{\partial\over \partial x}\ ... - {\partial\over \partial x}x\ ...## ?
     
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