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Questions about tensor operator

  1. May 14, 2014 #1
    Hi.
    Before question, sorry about my bad english. It's not my mother tongue.

    My QM textbook(Schiff) adopt

    J x J = i(h bar)J.

    as the defining equations for the rotation group generators in the general case.
    My question is, then tensor J must have one index which has three component? (e.g. x-y-z or rho-theta-z or r-theta-pi)

    And, i also have one question about position operator. In wikipedia, its eigen'value' is said to be particle's position 'vector'. What this mean is that position operator is (rank 3) tensor operator?

    Thanks for reading.
     
  2. jcsd
  3. May 14, 2014 #2

    Bill_K

    User Avatar
    Science Advisor

    Writing cross products of operators can be confusing, it's better to use the form in the previous equation, which uses commutation relations. Also, I would call this a property of angular momentum, not its definition. Schiff gives the definition a few equations earlier - the three components of angular momentum are defined to be the generators of infinitesimal rotations.

    Yes. A tensor operator with one index we call a vector operator.

    A vector operator, or rank 1 tensor. The rank of a tensor is the number of indices it has.
     
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