# What,s the meaning of

1. Apr 27, 2006

### eljose

is there (if any) a physical meaning to the function $$\nabla^{2}(S)$$ ?...we have that $$gra(S)=p$$ p=momentum vector my question is that somehow the operator proposed above is $$\nabla^{2}(S)=div(gra(S))=div(p)$$
although the proposed operator makes no sense in classical Hamilton-Jacobi Mechanics if we make the change of variable $$\Psi=e^{iS/\hbar}$$ inside SE equation you get the Pseudo-HJ equation:

$$dS/dt= (\nabla(S))^{2}+V(x,t)+U_{b}+i\hbar { \nabla^{2}(S) }$$ with m=1/2 and U_{b} is the Bohmian quantum potential.