1998/12/24 by Jerrold Franklin · 1 citation
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Coulomb #Coulomb wave function #Dirac equation #Electric potential #Electron #Ground state #Lorentz transformation #Mathematical physics #Physics #Quantum Mechanics and Non-Hermitian Physics #Quantum and Classical Electrodynamics #Quantum electrodynamics #Quantum mechanics #Scalar (mathematics) #Scalar potential #Simple (philosophy) #Wave function #hep-ph #nucl-th
paper · pdf · doi:10.1142/s0217732399002492
published as Mod.Phys.Lett. A14 (1999) 2409 · Misprints (mostly of sign) corrected in equations (8), (9), (13), (14), (18), and (21). No change in results or discussion
arxiv created 1998/12/24 · openalex publication_date 1999/11/10 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A simple analytical solution is found to the Dirac equation for the combination of a Coulomb potential with a linear confining potential. An appropriate linear combination of Lorentz scalar and vector linear potentials, with the scalar part dominating, can be chosen to give a simple Dirac wave function. The binding energy depends only on the Coulomb strength and is not affected by the linear potential. The method works for the ground state, or for the lowest state with l=j-1/2, for any j.