Derivation of a four-spinor Dirac-like equation for the helium atom and an approximate ground state solution

2013/10/26 by D. L. Nascimento, Daniel L. Nascimento, Nascimento, Daniel L. +3
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #FOS: Physical sciences #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph) #Quantum and Classical Electrodynamics #quant-ph

paper · pdf · doi:10.48550/arxiv.1310.7567

arxiv created 2013/10/26 · openalex publication_date 2013/10/26 · arxiv updated 2013/10/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We present a new analysis of the connection between the classical conservation theorems and the role played by the Dirac matrices in order to obtain a four spinor version of the Dirac equation for the two electrons bound problem. The separation of the set of equations in its angular and radial parts is done and an asymptotic solution for the radial system of equations is discussed for the ground state of the atom.

Related

• Conjugate Spinor Solution of the Dirac Equation for the Hydrogen Atom
• Solution of the Dirac-Coulomb equation using the Rayleigh-Ritz method. Results for He-like atoms
• General solution of the Dirac equation with the Coulomb potential
• Klein-Gordon and square-root operator equations for two-spinors and scalars: perturbation calculations for hydrogen-like systems
• On Dirac equation for a Coulomb scalar, vector, and tensor interaction