Klein Paradox for Bound States - a Puzzling Phenomenon

Abstract

While Klien paradox is often encountered in the context of scattering of relativistic particles at a potential barrier,we presently discuss a puzzling situation that arises with the Klien-Gordon equation for bound states. With the usual minimal coupling procedure of introducing the interaction potential, a paradoxical situation results when the "hill" becomes a "well" ,simulating a bound state like situation.This phenomenal phenomenon for bound states is contrary to the convectional wisdom of quantum mechanics and is analogous to the well-known Klien paradox,a generic property of relativistic wave equation.