# Satisfying Dirac equation, how to make equal to zero.

1. May 31, 2015

### rwooduk

1. The problem statement, all variables and given/known data

2. Relevant equations
Dirac equation: $$(\gamma ^{\mu}\rho_{\mu}-mc)\psi=0$$

3. The attempt at a solution
If we multiply out the Dirac equation by inserting all it's componants we get:

which if I've multiplied it correctly gives $$\begin{bmatrix} \frac{E}{c}-mc\\ 0 \\ \rho_{z} \\ \rho_{x}+i\rho_{y} \end{bmatrix}e^{-\frac{iEt}{\hbar}}=0$$

I'm not sure how to show the left hand side is equal to zero?

edit just realised that it is at rest so all the $\rho$ componants would be zero, but then I still dont see how E/c - mc multiplied by the exponential would give zero?

Any help / ideas would really be appreciated.

2. May 31, 2015

### Staff: Mentor

If the particle is at rest, what is its relation between energy and mass?

3. May 31, 2015

### rwooduk

ahhhh E=mc^2 so the term in the matrix would be zero, many thanks!!