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Dirac Equation - Analytic Solution?

  1. Aug 3, 2015 #1

    referframe

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    The quantum harmonic oscillator is an analytic solution of the Schrodinger Equation. Does the original Dirac Equation for a free electron also have an analytic solution? Of course a "solution" of the Dirac Equation would consist of 4 functions.

    Thanks in advance.
     
  2. jcsd
  3. Aug 3, 2015 #2

    MathematicalPhysicist

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    If there were such a solution you'd definitely would find it in Wiki entry.
     
  4. Aug 3, 2015 #3

    George Jones

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    Google

    "Dirac equation" hydrogen
     
  5. Aug 3, 2015 #4

    dextercioby

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    The harmonic oscillation is not modeled in the context of Dirac's equation, unless one leaves particle dynamics aside and does quantum field theory.
     
  6. Aug 4, 2015 #5

    fzero

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  7. Aug 4, 2015 #6

    Avodyne

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    Yes, if the potential energy is chosen to be ##\frac12 k x^2##.

    Now you've switched to a "free" electron, which means that the potential energy is zero. In this case, the general solution is a plane wave times a constant spinor; see fzero's link for details.
     
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