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Productrule on Operators

  1. Feb 6, 2014 #1
    Hey Guys,

    I regard two operators [itex]\Psi , \Phi [/itex], that don't commute.

    Does the product-rule, looks like that?

    $$\nabla (\Phi \Psi)

    = \Psi (\nabla \Phi)

    +\Phi (\nabla \Psi)


  2. jcsd
  3. Feb 6, 2014 #2


    User Avatar
    Gold Member

    How do you define the different items in this equation?
    For example if Ψ = ∇, how do you define ∇Ψ ?
    And in general?
  4. Feb 6, 2014 #3


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    Science Advisor

    You need to keep the original order:

    $$\nabla (\Phi \Psi) = (\nabla \Phi) \Psi+\Phi (\nabla \Psi) $$
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