On the common limit of the PT-symmetric rosen–morse II and finite square well potentials

József Kovács, Géza Lévai

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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.

Original languageEnglish
Pages (from-to)412-417
Number of pages6
JournalActa Polytechnica
Volume57
Issue number6
DOIs
Publication statusPublished - Jan 1 2017

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Keywords

  • Bound states
  • Dirac-δ limit
  • PT-symmetric potential
  • Scattering

ASJC Scopus subject areas

  • Engineering(all)

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