Let $\psi(x,t)=Ae^{i(kx-\omega t)}+ Be^{-i(kx+\omega t)}$. I am trying to find the probability current. http://en.wikipedia.org/wiki/Probability_current
I checked on wikipedia, and they give 2 formulas.
$$j = \frac{\bar h}{2mi}(\psi^*\frac{\partial\psi}{\partial x} - \psi \frac{\partial\psi^*}{\partial x})$$ $$j = \frac{\bar h}{2mi}(\psi^*\nabla\psi - \psi\nabla\psi^*)$$ and on another thread, the person uses $$j= \frac{i}{2}(\psi\partial_x\psi^*-\psi^*\partial_x\psi) \; ,$$ Probability flux
Which formula should I use?
If I want to find $\nabla\psi$, does it equals to $\nabla \psi = (\partial_x \psi, \partial_t \psi)$?