No abstract

By making use of the Hamilton-Jacobi equation, we obtain the exact value of the electronic energy levels for the heteromolecular ions HeH 2ϩ , LiH 3ϩ , and BeH 4ϩ as a function of nuclear distance. The Hylleraas method in association with the series established by Wind-Jaffé was applied to these molecular ions. The results are in good agreement with those found in the literature.

ABSTRACT:We provide a new analysis of the helium atom problem using Hamilton-Jacobi classical theory combined with the Sommerfeld quantization rule. The study is performed by reducing the three-body problem to an effective one-body problem, and it is shown that the theory is capable of reproducing (with a precision of 2%) the atomic ground-state binding energy. We have also obtained the exact asymptotic limit for the ground state of the helium ion.

ABSTRACT:In this article, we present a quantized classical-like wave equation. It is obtained by considering the equivalence between the Hamilton-Jacobi eq. (which belongs to the usual manifold R 3 R of General Relativity), with our two spinor versions of the Dirac eq. (which belongs to the associated complex manifold C C). In which the electron is considered as a particle-like entity, instead of the usual wave-like interpretation of standard Quantum Mechanics. We also consider the transformation properties between the two manifolds through the corresponding groups O(3,1) and SU(2), but we assume a flat Minkowsky space as the background space. We made an illustrative application to the rather standard problem of the hydrogen and helium atoms. We propose a variational extension of the approach, through a Hylleraas-like computational method, to take into account a many electron problem too futurely.

ABSTRACT:We present a method for solving many-body problems that allows the usage of Klein-Gordon-like equations and in which it is not necessary to take into account the spin of the particles, whose effect appears through orbital angular momentum. Hence, the method deals only with ordinary wavefunctions instead of the more complicated spinor wavefunctions of Dirac's theory. The general wave solutions are found to possess a very close resemblance to the corresponding classical solutions, which allow the usage of simple mechanic analogies to deal with the many-body problem. The method is applied to the H 2 ϩ molecule, yielding the correct value for the ground-state energy and also an approximation for the associated vibrational energies.