is there (if any) a physical meaning to the function [tex] \nabla^{2}(S) [/tex] ?...we have that [tex] gra(S)=p [/tex] p=momentum vector my question is that somehow the operator proposed above is [tex] \nabla^{2}(S)=div(gra(S))=div(p) [/tex](adsbygoogle = window.adsbygoogle || []).push({});

although the proposed operator makes no sense in classical Hamilton-Jacobi Mechanics if we make the change of variable [tex] \Psi=e^{iS/\hbar} [/tex] inside SE equation you get the Pseudo-HJ equation:

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

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# What,s the meaning of

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