Dirac Equation - Analytic Solution?

  • #1
referframe
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Main Question or Discussion Point

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.
 

Answers and Replies

  • #2
MathematicalPhysicist
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If there were such a solution you'd definitely would find it in Wiki entry.
 
  • #3
George Jones
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"Dirac equation" hydrogen
 
  • #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
Avodyne
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The quantum harmonic oscillator is an analytic solution of the Schrodinger Equation.
Yes, if the potential energy is chosen to be ##\frac12 k x^2##.

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.
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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