Semiclassical aspects and supersymmetry of bound Dirac states for central pseudo-scalar potentials

Authors: Thylwe, K.-E., Linnaeus, S.
Document Type: Article
Pubstate: Published
Journal: Physica Scripta
Volume: 84   025006
Year: 2011


Relativistic bound states for a linear, radial pseudo-scalar potential model are discussed. The two radial Dirac components are known to have a close connection to partner states in super-symmetric quantum mechanical theory. The pseudo-scalar potential plays the role of the ‘super potential’. Hence, the Dirac components satisfy decoupled Schro?dinger-type equations with isospectral, so-called, ‘partner potentials’ except possibly for a single state; the ground state corresponding to one of the partner potentials. The energy spectrum of a confining linear radial potential is discussed in some detail. Accurate amplitude-phase computations and a novel semiclassical (phase-integral) approach are presented.