New Relativistic Wave Equations for Two-Particle Systems

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 $\Psi ({\mathbf{r}}_1,{\mathbf{r}}_2,t)=\psi ({\mathbf{r}}_1,{\mathbf{r}}_2)e^{-iEt/\hslash },\psi ({\mathbf{r}}_1,{\mathbf{r}}_2)\in \mathcal{S}({\mathbb{R}}^3\times {\mathbb{R}}^3)$, and properly define the relativistic reduced mass ${\mu }_0$, 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 $\pi +$ and $\pi -$.

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

References in corpus (3)

• A New Operator Theory of Linear Partial Differential Equations
• Stationary Solutions of the Klein-Gordon Equation in a Potential Field
• Sommerfeld Fine-Structure Formula for Two-Body Atoms

Cited by in corpus (1)

• Nonlinear Klein-Gordon equation and the Bose-Einstein condensation