Hénon–Heiles interaction for hydrogen atom in phase space

Abstract

Using elements of symmetry, as gauge invariance, several aspects of a Schrödinger equation represented in phase-space are introduced and analyzed under physical basis. The Hydrogen atom is explored in the same context. Then we add a Hénon-Heiles potential to the Hydrogen atom in order to explore chaotic features.

Non-abelian Gauge Symmetry for Fields in Phase Space: a Realization of the Seiberg-Witten Non-abelian Gauge Theory

“…This has been accomplished [23,24], and in this approach, the Seiberg-Witten-gauge theory arises naturally by studying gauge transformations of the type ψ(q, p) → e −iλ(q,p) ⋆ψ(q, p), leading to a non-commutative-like electrodynamics, such that the propagators, describing bosons and fermions, are related to the Wigner function [21]. Applications of such results include: the interaction between the Dirac equation with an external electromagnetic field in phase space [30]; analysis of the Wigner function for the Landau problem [31]; evaluation of the negativity of the Wigner function for a system defined by the sum of Hénon-Heiles potential and Hydrogen atom [32]. Despite these advances with the field theory in phase phase, the non-abelian gauge symmetry has not been developed for fields in phase space.…”

Teoria quântica no espaço de fase : modelo de Hénon-Heiles e simetrias de calibre

“…Na proxima seção iremos calcular a função de Wigner para a correção de primeira ordem para a soma do potencial de Hénon-Heiles e o potencial do átomo de Hidrogênio em um campo magnético forte. Estes resultados encontra-se publicado em [66].…”