Conjugate Spinor Solution of the Dirac Equation for the Hydrogen Atom

2011/04/18 by R. Ducharme, Ducharme, Robert J.
Physics and Astronomy · #Experimental and Theoretical Physics Studies #FOS: Physical sciences #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph) #Quantum and Classical Electrodynamics

paper · pdf · doi:10.48550/arxiv.1104.3377

openalex publication_date 2011/04/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is shown the central field Dirac equation can be simplified through the use of real conjugate spinors to substitute for the upper and lower components of the bi-spinor eigensolutions. This substitution reduces the Dirac equation for the hydrogen atom to the problem of solving a single second order differential equation similar to a Klein-Gordon equation but containing additional terms to take account of the spin on the electron. The bi-spinor wave functions are readily constructed once the solution is known in terms of the conjugate spinors.

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