Abstract
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.
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M.Born zum 80. Geburtstag gewidmet.
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Beck, F., Steinwedel, H. & Süssmann, G. Bemerkungen zum Kleinschen Paradoxon. Z. Physik 171, 189–198 (1963). https://doi.org/10.1007/BF01379347
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DOI: https://doi.org/10.1007/BF01379347