Spin and pseudospin symmetries and the equivalent spectra of relativistic spin-1/2 and spin-0 particles

Abstract

We show that the conditions which originate the spin and pseudospin symmetries in the Dirac equation are the same that produce equivalent energy spectra of relativistic spin-1/2 and spin-0 particles in the presence of vector and scalar potentials. The conclusions do not depend on the particular shapes of the potentials and can be important in different fields of physics. When both scalar and vector potentials are spherical, these conditions for isospectrality imply that the spin-orbit and Darwin terms of either the upper component or the lower component of the Dirac spinor vanish, making it equivalent, as far as energy is concerned, to a spin-0 state. In this case, besides energy, a scalar particle will also have the same orbital angular momentum as the (conserved) orbital angular momentum of either the upper or lower component of the corresponding spin-1/2 particle. We point out a few possible applications of this result.

arXiv comment5 pages, uses revtex macros

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• Spin and Pseudospin symmetries in the Dirac equation with central Coulomb potentials
• Exact Solutions of the Klein-Gordon Equation with Hylleraas Potential
• Higgs algebraic symmetry in the two-dimensional Dirac equation
• Approximate bound states of the Dirac equation with some physical quantum potentials
• Dynamical symmetry of Dirac hydrogen atom with spin symmetry and its connection with Ginocchio's oscillator
• Scattering of Klein-Gordon particles in the background of mixed scalar-vector generalized symmetric Woods-Saxon potential
• An Investigation of the Bound State Solutions of the Klein-Gordon Equation for the Generalized Woods-Saxon Potential in Spin Symmetry and Pseudo-spin Symmetry Limits
• Relativistic particle in a box: Klein-Gordon vs Dirac Equations
• Standard and helical magnetorotational instability: How singularities create paradoxal phenomena in MHD
• Dynamical symmetries of the Klein-Gordon equation
• Approximate Dirac solutions of complex -symmetric Pöschl-Teller potential in view of spin and pseudospin symmetries
• Scattering and bound states of spinless particles in a mixed vector-scalar smooth step potential
• General spin and pseudospin symmetries of the Dirac equation
• New solutions of the D-dimensional Klein-Gordon equation via mapping onto the nonrelativistic one-dimensional Morse potential
• Bound states of bosons and fermions in a mixed vector-scalar coupling with unequal shapes for the potentials
• Stationary states of fermions in a sign potential with a mixed vector-scalar coupling
• Scattering and bound states of fermions in a mixed vector-scalar smooth step potential
• Quadratic Algebra Approach to Relativistic Quantum Smorodinsky-Winternitz Systems
• Relativistic Coulomb scattering of spinless bosons
• Unsuitable use of spin and pseudospin symmetries with a pseudoscalar Cornell potential
• Correction to Solution of Dirac Equation
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• Solutions of the spatially-dependent mass Dirac equation with the spin and pseudo-spin symmetry for the Coulomb-like potential
• Fermions embedded in a scalar-vector kink-like smooth potential