On the common limit of the pt-symmetric rosen–morse ii and finite square well potentials

József Kovács, Géza Lévai

On the common limit of the pt-symmetric rosen–morse ii and finite square well potentials

Číslo: 6/2017
Periodikum: Acta Polytechnica
DOI: 10.14311/AP.2017.57.0412

Klíčová slova: PT-symmetric potentials, bound states, scattering, Dirac-delta limit, PT-symetrické potenciály, vázané stavy, rozptyl, Dirac-delta limit

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Anotace: 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.