Hamilton –Jacobi theorem and Information geometry of Quantum Mechanics

Abstract

In this research we consider the stander formulation of the Hamilton-jacobi and the hydrodynamical formulation of quantum mechanics problems.For these we discuss the development of the Hamilton-jacobi theory for singular lagrangian systems in the skinner- rsuk formulism,and then we discuss it´s comparisons with the Hamilton-jacobi problem in the lagrangian and Hamiltonian setting. Also we illustrate that the frechet manifold of smooth probability density function is equipped with a Reimannian metric and affine connection which are infinite dimensional analogues of the fisher metric and exponential connection in the context of information geometry