Dynamical symmetry of Dirac hydrogen atom with spin symmetry and its connection with Ginocchio's oscillator

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.

arXiv comment3 pages,Accepted by PRA as a Rapid Communication

References in corpus (6)

• Pseudo-spin as a Relativistic Symmetry
• Dirac and Klein-Gordon equations with equal scalar and vector potentials
• Spin symmetry in the anti-nucleon spectrum
• Relativistic Harmonic Oscillator with Spin Symmetry
• U(3) and Pseudo-U(3) Symmetry of the Relativistic Harmonic Oscillator
• Spin and pseudospin symmetries and the equivalent spectra of relativistic spin-1/2 and spin-0 particles

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• Scattering and bound states of fermions in a mixed vector-scalar smooth step potential
• Quadratic Algebra Approach to Relativistic Quantum Smorodinsky-Winternitz Systems
• Symmetry of Dirac Equation and Corresponding Phenomenology
• Unsuitable use of spin and pseudospin symmetries with a pseudoscalar Cornell potential
• Dynamical Algebras in the 1+1 Dirac Oscillator and the Jaynes-Cummings Model
• Re-study on the contribution of scalar potential and spectra of $c\bar{c}$, $b\bar{b}$ and $b\bar{c}(\bar{b}c)$ families
• Dynamical Symmetries of Dirac Hamiltonian