the probability current density

Question

show that if S(r,t) is defined by Ψ= exp (i S 2 bi/h) the probability current density can be expressed as j= ρ∇ (Re S)/ m

Answer 1

this is a standard problem in quantum mechanics...

 

Start with the definition of current density and simply substitude wavefunction..

 

see link for derivation.

 

https://en.wikipedia.org/wiki/Probability_current