Quantum bifurcation in a coulombic-like potential

Ciann Dong Yang, Hung Jen Weng

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

Because of the lack of nonlinear dynamics, up to now no bifurcation phenomenon in its original sense has been discovered directly in quantum mechanical systems. Based on the formalism of complex-valued quantum mechanics, this article derives the nonlinear Hamilton equations from the Schrödinger equation to provide the necessary mathematic framework for the analysis of quantum bifurcation. This new approach makes it possible to identify quantum bifurcation by the direct evidence of the sudden change of fixed points and their surrounding trajectories. As a practical application of the proposed approach, we consider the quantum motion in a Coulombic-like potential modeled by V(r) = A/r2 - B/r, where the first term describes the centrifugal trend and the second deals with the Coulombic attraction. As the bifurcation parameter evolves, we demonstrate how local and global bifurcations in quantum dynamics can be identified by inspecting the changes of fixed points and their surrounding trajectories.

Original languageEnglish
Pages (from-to)4330-4351
Number of pages22
JournalInternational Journal of Quantum Chemistry
Volume111
Issue number15
DOIs
Publication statusPublished - 2011 Dec

All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics
  • Condensed Matter Physics
  • Physical and Theoretical Chemistry

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