New Relativistic Wave Equations for Two-Particle Systems

Details New Relativistic Wave Equations for Two-Particle Systems New Relativistic Wave Equations for Two-Particle Systems

2012-04-22

arxiv.org/abs/1204.4876v1

Physics

Mathematical Physics

27 pages. arXiv admin note: substantial text overlap with arXiv:1008.4224

Scientific paper

We seek to introduce a mathematical method to derive new relativistic wave equations for two-particle systems. According to this method, if we define stationary wave functions as special solutions like $\Psi(\mathbf{r}_1, \mathbf{r}_2,t) = \psi(\mathbf{r}_1, \mathbf{r}_2) e^{-iEt/\hbar}$, and properly define the relativistic reduced mass $\mu_0$, then the relativistic correction of the Schr\"{o}dinger equation for two-particle system can be derived. The spin-orbit coupling term is also derived from the relativistic correction terms. On this basis, we obtain the relativistic energy levels of pionium and pionic hydrogen atoms, using which, we discuss the pair production and annihilation of $\pi+$ and $\pi-$, and find a reasonable explanation for dark energy and dark matter.

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