Bemerkungen zum Kleinschen Paradoxon

The problem of stationary energy eigenstates of relativistic spin 1/2-particles in external potentials exceeding twice the particles rest mass (Klein's paradox) is investigated, neglecting the interaction of the particles with the radiation field. This corresponds to theH ₀ of the “bound state interaction representation” in quantum electrodynamics. For simplicity, explicit calculations are based on a one dimensional square well potential. In potentials of this type which vanish at infinity and which do not become critically singular at the origin there always exists a stationary ground state of fixed total charge. Though this state, naturally, cannot be attributed to a sharp number of particles, no real paradox occurs.