# Probability current density

1. Sep 16, 2007

### qwijiboo

Hi folks!

Can someone tell me how to solve the following... I'd really appreciate it.

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

Show that the below two expressions for probability current density are equivalent.

j(r,t) = h'/2im($$\Psi^{*}$$$$\Delta\Psi$$- ($$\Delta\Psi^{*}$$)$$\Psi$$]

j(r,t) = real part of [$$\Psi^{*}$$ (h'/im) $$\Delta\Psi$$]

2. Relevant equations
h' is the reduced plancks constant h/2pi

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Sep 16, 2007

### Dick

You should really give us your thoughts (or at least a guess) on this. But if c is a complex number, what's the relation between Im(c) and Re(c/i)? And you may also want to think about integration by parts.

3. Sep 17, 2007

### qwijiboo

I'm sorry... but I figured it out. Its a pure math problem. Sometimes my brain just ceases to work!!!

RP of the second equation is {j(r,t) + [j(r,t)]*}/2 substituting ,we get the first equation.

Thanks anyways for replying to my post.