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Momentum operator's relation to commutative algebra

  1. May 17, 2012 #1
    how is the quantum momentum operator (being a linear differential op.) related to commutative algebra?
     
  2. jcsd
  3. May 17, 2012 #2

    strangerep

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    (Linear) momentum operators corresponding to independent directions commute.
     
  4. May 17, 2012 #3
    Does the momentum operator by itself carry information about direction?
    Or does the operator obtain it from the wavefunction?
     
  5. May 17, 2012 #4
    What commutative algebra?
     
  6. May 17, 2012 #5

    dextercioby

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    It's customary to call them Abelian algebras.
     
  7. May 17, 2012 #6

    strangerep

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    A (linear) momentum operator generates translations along a particular direction in space.
    (I'm not sure what your background is. Normally I recommend Ballentine's textbook.)
     
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