How Do You Derive the Relativistic Probability Current Formula?

[opous]

[SOLVED] Relativistc probability current

Homework Statement

I've got two formulae here and I'm not sure how you get from the first to the second:

$$\textbf{j}(\textbf{x},t) = Re[\Psi^{*}(x,t)(-i/m)\nabla\Psi(x,t)]$$

$$= \frac{-i}{2m}[\Psi^{*}(\nabla\Psi) - (\nabla\Psi^{*})\Psi]$$

Can anyone suggest a relationship I need to bridge the gap? Thanks.

Homework Equations

The Attempt at a Solution

 

[Dick]

Try Re(z)=(z+z*)/2.

 

[opous]

Got it! Thanks Dick :)