## Hydrogen Atom Set up by Electron Capture Describing a Continuous Path

In the creation of a hydrogen atom, we present a formulation in which an electron may follow a continuous path. To form electron motion, we use a field Lagrangean basis for chaotic, non-conservative systems. In the case of the proton-nucleus, we discovered electron transition paths ranging from infinity to finite radii, which correspond to stable orbital states. In the chaotic dynamical motion problem, finding these states corresponds to finding the possible stable orbital attractors. Although the electron-proton system has a general collapsing tendency, the Hamiltonian of the system exhibits several metastable states in which the electron will remain for a finite amount of time due to the chaotic perturbations that the electron undergoes during atom forming. The Hamiltonian shifts along the electron course, from zero at infinity to negative values corresponding to certain metastable orbits.

**Author (s) Details**

**D. L. Nascimento
**Institute of Physics, University of Brasília, 70919-970 Brasília – DF, Brazil.

**A. L. A. Fonseca
**Institute of Physics, University of Brasília, 70919-970 Brasília – DF, Brazil and International Center for Condensed Matter, University of Brasília, 70919-970 Brasília – DF, Brazil.

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Chaos electron capture in hydrogen atom electron path Lagrangean systems non-conservative orbital systems nonlinear dynamics quantum physics. stable attractors