New approach using the relativistic Hamilton–Jacobi equation to evaluate the correct energy levels for the hydrogen atom

The aim of the present study is to propose a model based on classical field theory to study atomic and molecular systems. Starting from the basic principles of the special relativity theory (SRT), the model is described by taking the interaction between two moving particles with the standing wave radiated from the particles in the four-dimensional space–time. According to the classical theory of fields, the geometrical properties of the solutions are governed by a classical-like equation of motion. An eigenvalue equation is derived from an improvement of the relativistic variational method introduced by Schrödinger in 1926 1. This formalism is applied to the standard hydrogen atom problem, yielding solutions of the equation of motion by integrals of action and by solving the associated differential eigenvalue equation. Both sets of solutions reproduce the correct fine structure of the energy levels. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006