Applications of a property of the Schrodinger equation to the modeling of conservative discrete systems. III

We have demonstrated in previous papers the following property of closed, c onservative and bounded systems: The energy which results from the Schrodin ger equation can be rigorously calculated by line integrals of analytical f unctions, if the Hamilton-Jacobi equation, written for the same system, is satisfied in the space of coordinates by a periodical trajectory. In the pr esent article. we show that this property is connected to the intrinsic wav e properties of the system. This results from the equivalence between the S chrodinger equation and the wave equation, valid for conservative systems. As a consequence of the wave properties of the system, we show that the Ham ilton-Jacobi equation has always periodical solutions, whose constants of m otion are identical to the eigenvalues of the Schrodinger equation, written for the same system. It results that the calculation model presented in pr evious papers is generally valid in the case of closed, conservative and bo unded systems. We present the applications of the model to the nitrogen and oxygen atoms, to the ions with the same structure, and to the He-2, Be-2 a nd B-2 molecules.