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Commutator [x,T]?

  1. Jun 26, 2014 #1
    1. The problem statement, all variables and given/known data

    Find ##[\hat{x},\hat{T}]##.

    2. Relevant equations

    ##[\hat{x},\hat{T}]=\hat{x}\hat{T}-\hat{T}\hat{x}##

    3. The attempt at a solution
    I wind up with ##\frac{i\hbar}{m}\hat{p}##. Did I do good, boss?

    Chris
     
  2. jcsd
  3. Jun 26, 2014 #2

    Dr Transport

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    Science Advisor
    Gold Member

    Define [itex] \hat{T}[/itex]
     
  4. Jun 26, 2014 #3
    It is the kinetic energy operator. p^2/2m.

    Chris
     
  5. Jun 27, 2014 #4

    CAF123

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    Gold Member

    Your answer is correct.

    I am not sure if this is the way you did it, but using the fact that ##[A,BC] = B[A,C] + [A,B]C## for operators ##A, B## and ##C##, the result follows in one line using the canonical commutation relations for ##\hat{x}## and ##\hat{p}##.
     
    Last edited: Jun 27, 2014
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