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One-particle Dirac and KG equations

  1. Feb 10, 2006 #1
    So there's something I don't quite understand.

    The density in the KG equation stands for charge density. Here are several questions:

    1. For a KG particle, how do I (if it all) find the position probabilty density?
    2. For a Dirac particle, what does the (now positive definite) density stand for?
    3. For a now KG or Dirac field, is there no position probability density?
  2. jcsd
  3. Feb 11, 2006 #2

    Meir Achuz

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    In the Dirac equation |\psi|^2 is the position probability, just as in the Schrodinger Eq. The KG equation has a problem. The one particle solution does not conserve probablility for \phi^*\phi. One (not too satisfactory) solution of this is to call it charge density. The real way out is to second quantize the KG equation, leadilng to QFT. Then, the KG
    operator is an operator on a new wave function. The same second quantization can be applied to the Schrodingeer and the Dirac equations.
    You need a book beyond the first level QM for this.
    I like one by Halzen and Martin, but there are several.
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