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arXiv:1502.04838 · Physics Letters A

A new solvable complex PT-symmetric potential

Zafar Ahmed, D. C. Ghosh, Joseph Amal Nathan

Published Apr 25, 2015• 12 citations
arXivHTMLPDF
DOI
10.1016/j.physleta.2015.04.032

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Algebraic and scattering aspects of a 𝒫𝒯-symmetric solvable potential

GÉZA LÉVAI, F. Cannata, Alberto Ventura

We study a particular solvable potential and analyse the effect of 𝒫𝒯 symmetry on its bound state as well as scattering solutions. We determine the transmission and reflection coefficients for the 𝒫𝒯-symmetric case and also formulate the problem in terms of an SU (1,1) potential group, which allows unified treatment of the discrete and the continuous spectra in a natural way. We find that (bound and scattering) states of the 𝒫𝒯-symmetric problem supply a basis for the unitary irreducible representations of the SU (1,1) potential group, and this gives a straightforward group theoretical interpretation of the fact that the (complex) 𝒫𝒯-invariant potential has a real energy spectrum.

Journal of Physics A Mathematical and General•Jan 18, 2001•82 citations
We study a particular solvable potential and analyse the effect of 𝒫𝒯 symmetry on its bound state as well as scattering solutions. We determine the transmission and reflection coefficients for the 𝒫𝒯-symmetric case and also formulate the problem in terms of an SU (1,1) potential group, which allows unified treatment of the discrete and the continuous spectra in a natural way. We find that (bound and scattering) states of the 𝒫𝒯-symmetric problem supply a basis for the unitary irreducible representations of the SU (1,1) potential group, and this gives a straightforward group theoretical interpretation of the fact that the (complex) 𝒫𝒯-invariant potential has a real energy spectrum.