Sameer M. Ikhdair, Majid Hamzavi

By employing an exponential-type approximation scheme to replace the centrifugal term, we have approximately solved the Dirac equation for spin-particle subject to the complex-symmetric scalar and vector Poschl-Teller (PT) potentials with arbitrary spin-orbit -wave states in view of spin and pseudospin (p-spin) symmetries. The real bound-state energy eigenvalue equation and the corresponding two-spinor components wave function expressible in terms of the hypergeometric functions are obtained by means of the wave function analysis. The spin-Dirac equation and the spin-Klein-Gordon (KG) equation with the complex Poschl-Teller potentials share the same energy spectrum under the choice of (i.e., exact spin and p-spin symmetries).

http://arxiv.org/abs/1208.4960

Quantum Physics (quant-ph); Mathematical Physics (math-ph)

Francisco Correa, Mikhail S. Plyushchay

The origin of spectral singularities in finite-gap singly periodic PT-symmetric quantum systems is investigated. We show that they emerge from a limit of band-edge states in a doubly periodic finite gap system when the imaginary period tends to infinity. In this limit, the energy gaps are contracted and disappear, every pair of band states of the same periodicity at the edges of a gap coalesces and transforms into a singlet state in the continuum. As a result, these spectral singularities turn out to be analogous to those in the non-periodic systems, where they appear as zero-width resonances. The specific degeneration related to the presence of finite number of spectral singularities in periodic quantum systems with compact and non-compact topologies is shown to be coherently reflected by a hidden, bosonized nonlinear supersymmetry.

http://arxiv.org/abs/1208.4448

High Energy Physics – Theory (hep-th); Mathematical Physics (math-ph); Quantum Physics (quant-ph)