Title: The Klein Paradox: A New Treatment,
Abstract: The Dirac equation requires a treatment of the step potential that differs
fundamentally from the traditional treatment, because the Dirac plane waves,
besides momentum and spin, are characterized by a quantum number with the
physical meaning of sign of charge. Since the Hermitean operator corresponding
to this quantum number does not commute with the step potential, the time
displacement parameter used in the ansatz of the stationary state does not have
the physical meaning of energy. Therefore there are no paradoxal values of the
energy. The new solution of the Dirac equation with a step potential is
obtained. This solution, again, allows for phenomena of the Klein paradox type,
but in addition it contains a positron amplitude localized at the threshold
point of the step potential.