Bound states by a pseudoscalar Coulomb potential in 1+1 dimensions

Abstract

The Dirac equation is solved for a pseudoscalar Coulomb potential in a two-dimensional world. An infinite sequence of bounded solutions are obtained. These results are in sharp contrast with those ones obtained in 3+1 dimensions where no bound-state solutions are found. Next the general two-dimensional problem for pseudoscalar power-law potentials is addressed consenting us to conclude that a nonsingular potential leads to bounded solutions. The behaviour of the upper and lower components of the Dirac spinor for a confining linear potential nonconserving- as well as conserving-parity, even if the potential is unbounded from below, is discussed in some detail.

18 pages, 6 figures

References in corpus (4)

• One-dimensional Dirac oscillator in a thermal bath
• Confinement of fermions by mixed vector-scalar linear potentials in two-dimensional space-time
• Confinement of neutral fermions by a pseudoscalar double-step potential in (1+1) dimensions
• Scattering of neutral fermions by a pseudoscalar potential step in two-dimensional space-time

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