New Relativistic Wave Equations for Two-Particle Systems

Publication date: 22 April 2012

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

P s i (m a t h b f r_{1}, m a t h b f r_{2}, t) = p s i (m a t h b f r_{1}, m a t h b f r_{2}) e^{- i E t / h b a r},, p s i (m a t h b f r_{1}, m a t h b f r_{2}) i n m a t h s c r S (m a t h b b R^{3} i m e s m a t h b b R^{3})

, and properly define the relativistic reduced mass

m u_{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

p i +

and

p i -

.

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