# Quick question on Probability Current

1. Aug 14, 2013

### Seydlitz

Here's the probability current equation as seen in Griffith's book.

$$j = \frac{\hbar}{2mi}\left(\Psi^* \frac{\partial \Psi }{\partial x}- (\frac{\partial \Psi^* }{\partial x})\Psi \right)$$

Does the second right term instruct us to take the derivative of the wave function complex conjugate? Or for that matter $$\Psi^*$$ this refers to the complex conjugate right?

Secondly, what math topics are included in Schrodinger's equation? Is it only differential calculus or does it also include complex variable calculus?

Thank You

2. Aug 14, 2013

### vanhees71

Since $t \in \mathbb{R}$, of course
$$\frac{\partial \psi^*}{\partial t}=\left (\frac{\partial \psi}{\partial t} \right )^*.$$
In principle the SchrÃ¶dinger equation is a partial differential equation of real arguments for a complex-valued function.

Of course, as always, the use of complex analysis is of great advantage to find solutions. The masters of this approach were Sommerfeld and Pauli. You can read about this in Pauli's marvelous lectures on the subject.

3. Aug 14, 2013

### Seydlitz

Ok thank you for the information. Should I read some math books about complex analysis or does the basic technique usually discussed in normal calculus books? Where can you watch Pauli's lecture on this?