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Separating operators into classical + quantum

  1. Feb 11, 2013 #1

    DrClaude

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    In the paper http://link.aps.org/doi/10.1103/PhysRevA.85.062329, the authors separate the position and momentum operators into classical motion and quantum fluctuations:
    [tex]\hat{X}_i \equiv \bar{X}_i + \hat{q}_i; \quad \hat{P}_i \equiv \bar{P}_i + \hat{\pi}_i[/tex]
    Can someone point me to a reference rigorously explaining why and how this can be done?
     
  2. jcsd
  3. Feb 11, 2013 #2

    Bill_K

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    Can you give more details? There's no way to tell from what you have written what is going on.
     
  4. Feb 11, 2013 #3

    DrClaude

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    That is exactly the problem I have.

    Apart from quoting the article I linked to, there is not much more I can do. [itex]\bar{X}_i[/itex] is the "classical position" of the [itex]i[/itex]th particle, but I do not understand how to express the operators [itex]\bar{X}[/itex], [itex]\hat{q}[/itex], etc.
     
  5. Feb 11, 2013 #4

    stevendaryl

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    What I've seen some people do in the path-integral formulation of quantum mechanics is to split the path into a sum of the classical path + a quantum correction. I assume that you can do the same thing with operators in the Heisenberg picture (where instead of operators that are time-independent and states that are time-dependent, it's the other way around).
     
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