ON THE COMMON LIMIT OF THE PT-SYMMETRIC ROSEN–MORSE II AND FINITE SQUARE WELL POTENTIALS

József Kovács, Géza Lévai

Abstract


Two PT-symmetric potentials are compared, which possess asymptotically finite imaginary components: the PT-symmetric Rosen-Morse II and the finite PT-symmetric square well potentials. Despite their different mathematical structure, their shape is rather similar, and this fact leads to similarities in their physical characteristics. Their bound-state energy spectrum was found to be purely real, an this finding was attributed to their
asymptotically non-vanishing imaginary potential components. Here the V(x)= γδ(x)+ i2Λ sgn(x) potential is discussed, which can be obtained as the common limit of the two other potentials. The energy spectrum, the bound-state wave functions and the transmission and reflection coefficients are studied in the respective limits, and the results are compared.

Keywords


PT-symmetric potentials, bound states, scattering, Dirac-delta limit

Refbacks

  • There are currently no refbacks.


Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

ISSN 1210-2709 (Print)
ISSN 1805-2363 (Online)
Published by the Czech Technical University in Prague