Open AccessA relativistic non-harmonic oscillator potential and pseudospin symmetry
Author(s) -
Min-Cang Zhang
Publication year - 2009
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.58.61
Subject(s) - physics , harmonic oscillator , hamiltonian (control theory) , dirac equation , spinor , quantum mechanics , scalar (mathematics) , bound state , wave function , harmonic potential , mathematical physics , symmetry (geometry) , relativistic wave equations , quantum electrodynamics , mathematics , mathematical optimization , geometry
A generalized non-harmonic oscillator potential for spin 1/2 particles is studied. The Dirac Hamiltonian contains a scalar and a vector non-harmonic oscillator potentials. Setting either or both combinations Σ(r)=S(r)+V(r) and Δ(r)=V(r)-S(r) to zero, analytical solutions for bound states of the corresponding Dirac equation are found. The eigenenergies and wave functions are presented, showing the pseudospin symmetry exists exactly.The relations between radial nodes of upper and lower components of the Dirac spinor are obtained.