Let be the S function being the action in physics S=S(x,y,z,t) satisfying the equation:
\frac{dS}{dt}+(1/2m)(\nabla{S})^{2}+V(x,y,z,t)=0
where V is the potential is there any solution (exact) to it depending on V?
let be (dS/dt)+(gra(S))^2/2m+(LS)+V(x) where L is the Laplacian Operator and V is the potential...could it be considered as the Hamiltan Jacobi equation for a particle under a potential Vtotal=V(x)+(LS) where S is the action