NEW CONNECTIONS BETWEEN QUANTUM AND CLASSICAL EQUATIONS WITH APPLICATIONS TO THE MODELING OF ATOMIC, MOLECULAR AND ELECTRODYNAMICAL SYSTEMS
Alexandru Popa
In previous papers we proved the existence of exact connections between quantum and classical equations in the cases of two different quantum systems, namely the stationary atomic and molecular systems and the systems composed by electrons and very intense electromagnetic field. We proved that the geometrical elements of the wave described by the Schrodinger equation, namely the characteristic surfaces and curves, denoted, respectively, by Σ and C, are solutions of the HamiltonJacobi equations, written for the same system, in the case of multidimensional stationary systems. The Σ surfaces, which have the significance of wave surfaces, and the C curves, which are their normals, correspond to the same constants of motion as the eigenvalues of the Schrodinger equation. In three recent papers we presented a central field method for the calculation of the C curves, and of the corresponding energetic values. We have verified this method for a large number of atoms and diatomic molecules, and we found that its accuracy is comparable to the accuracy of the Hartree-Fock method applied to the same atoms and diatomic molecules. In another papers we proved that the Klein-Gordon equation for the system electron-very intense electromagnetic field is verified exactly by the function associated to the classical motion of the electron. An exact connection follows between the solutions of the Klein-Gordon and the relativistic Hamilton-Jacobi equations, for that system. This result explains the accuracy of numerous classical models from the literature, belonging to the new field studying the interactions between very intense laser beams and electron plasmas. We present now a short review of these results.
•Jan 1, 2011•2 citations