Algebraic and scattering aspects of a 𝒫𝒯-symmetric solvable potential
- 18 January 2001
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 34 (4), 839-844
- https://doi.org/10.1088/0305-4470/34/4/310
Abstract
We study a particular solvable potential and analyse the effect of symmetry on its bound state as well as scattering solutions. We determine the transmission and reflection coefficients for the -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 -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) -invariant potential has a real energy spectrum.Keywords
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