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Operator Properties

  1. Mar 10, 2014 #1
    1. The problem statement, all variables and given/known data
    I am solving a problem and I arrived near the end, and can't figure out what to do here:

    (1/(2m)) [P^2,X]+[P^2,X]

    m - mass
    P - Momentum operator
    X - Position operator


    2. Relevant equations

    P = -iħ(∂/∂x)
    [A,B]=AB-BA
    [AB,C]=A[B,C]+B[A,C] where A, B and C are any operators

    3. The attempt at a solution

    I used [AB,C]=A[B,C]+B[A,C] to get 1/2m (P(PX-XP) + (PX-XP)P) and blocked
     
  2. jcsd
  3. Mar 10, 2014 #2

    strangerep

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    Science Advisor

    For an arbitrary wavefunction ##\psi(x)##, what is ##P\psi## and ##X\psi##? If you can figure those out, then you should be able to figure out ##[X,P]\psi## ...
     
  4. Mar 11, 2014 #3

    vanhees71

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    Science Advisor
    2016 Award

    The correct formula is
    [tex][AB,C]=A[B,C]+[A,C]B.[/tex]
     
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