# Pair production bound states

1. Apr 19, 2010

### FunkyDwarf

Hey Guys,

Am working through Relativistic Quantum Mechanics: Wave equations by W.Greiner and have a simple question about the Klein-Gordon equation: is it fair to say that bound states only occur between -m<=E<=m? (c=1). There are a few problems where they show that you can get pair production when the energy of the bound state is -m, and go on to comment about 'diving into the lower continuum'. However, in say the finite coulomb case, if one takes the exterior wave equation, which is just the basic Coulomb problem with a -1/r potential, then the asymptotic behaviour suggests that you only get exponential soltions, ie bound states, in the range described above and not for energies more negative than that.

Are they postulating on more negative bound states purely by extrapolation or is there a way to solve for bound states whos energies are <-m? I know this is somewhat unphysical as one must consider pair production, but just as an academic exercise will those states come out of the mathematics, as i can't see how they would :(

Cheers!
-G