# Dirac Equation - Analytic Solution?

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1. Aug 3, 2015

### referframe

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. Aug 3, 2015

### MathematicalPhysicist

If there were such a solution you'd definitely would find it in Wiki entry.

3. Aug 3, 2015

### George Jones

Staff Emeritus
Google

"Dirac equation" hydrogen

4. Aug 3, 2015

### dextercioby

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

5. Aug 4, 2015

6. Aug 4, 2015

### Avodyne

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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