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Commutator of [x,p e^(-p) ]

  1. Jun 16, 2015 #1
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    1. The problem statement, all variables and given/known data
    commutator of [x,p e^(-p) ]

    2. Relevant equations

    3. The attempt at a solution
    answer is i - i.e^(-p)
  2. jcsd
  3. Jun 16, 2015 #2


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    what is p in the e^(-p)?
  4. Jun 16, 2015 #3
    If it's the usual notation for quantum mechanics, x is position and p is momentum.
  5. Jun 16, 2015 #4
    its just the usual commutation relation of x and p with e^(-p) in multiplication.
    the method of solving remains the same.
  6. Jun 16, 2015 #5


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    I will assume that the multiplicative factor which should exist next to the momentum in the exponential in order to conform with the dimensionality is presumed to be unity. There is a shortcut formula for calculating commutators of the form [x,f(p)] and [p,g(x)]. In case you never heard about it, you should then do the calculation by first expanding ##e^{-p}## into power series and use the fundamental commutation relation between x and p.
  7. Jun 18, 2015 #6


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