New Relativistic Wave Equations for Two-Particle Systems

2012/04/22 by Guang-Qing Bi, Guangqing Bi, Bi, Guangqing +2
Mathematics · Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum and Classical Electrodynamics #Relativity and Gravitational Theory #Scientific Research and Discoveries #hep-th #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.1204.4876

25 pages. arXiv admin note: text overlap with arXiv:1008.4224

openalex publication_date 2012/04/22 · arxiv created 2013/10/05 · arxiv updated 2013/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We seek to introduce a mathematical method to derive the relativistic wave equations for two-particle system. According to this method, if we define stationary wave functions as special solutions like Ψ(r₁,r₂,t)=ψ(r₁,r₂)e^-iEt/ℏ, ψ(r₁,r₂)∈\mathscrS (ℝ³×ℝ³), and properly define the relativistic reduced mass μ₀, then some new relativistic two-body wave equations can be derived. On this basis, we obtain the two-body Sommerfeld fine-structure formula for relativistic atomic two-body systems such as the pionium and pionic hydrogen atoms bound states, using which, we discuss the pair production and annihilation of π+ and π-.

Citations

• Stationary Solutions of the Klein-Gordon Equation in a Potential Field
• A New Operator Theory of Linear Partial Differential Equations

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