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Parity operator commutes with second derivative?

  1. Jan 28, 2015 #1
    How do I prove that the parity operator Af(x) = f(-x) commutes with the second derivative operator. I am tempted to write:

    A∂^2f(x)/∂x^2 = ∂^2f(-x)/∂(-x)^2 = ∂^2f(-x)/∂x^2 = ∂^2Af(x)/∂x^2

    But that looks to be abuse of notation..
  2. jcsd
  3. Jan 29, 2015 #2


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    Staff: Mentor

    You can do both differentiations separately, then it does not look so bad any more.
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