Dynamical symmetry of Dirac hydrogen atom with spin symmetry and its connection with Ginocchio's oscillator
Fu-Lin Zhang, Bo Fu, Jing-Ling Chen
TL;DR
This paper demonstrates that the Dirac hydrogen atom with spin symmetry exhibits SO(4) symmetry, derives its generators, and connects it to a four-dimensional Dirac oscillator system via a specific transformation.
Contribution
It reveals the SO(4) symmetry of the Dirac hydrogen atom with spin symmetry and links it to a four-dimensional Dirac oscillator through the Kustaanheimo-Stiefel transformation.
Findings
Derivation of SO(4) symmetry generators for the Dirac hydrogen atom with spin symmetry.
Natural derivation of the energy spectrum from the Casimir operator.
Connection established between the hydrogen atom and a four-dimensional Dirac oscillator system.
Abstract
The Dirac hydrogen atom with spin symmetry is shown has a SO(4) symmetry. The generators are derived, and the corresponding Casimir operator leads to the energy spectrum naturally. This type hydrogen atom is connected to a four-dimensional Dirac system with equal scalar and vector harmonic oscillator potential, by the Kustaanheimo-Stiefel transformation with a constraint.
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