Supersymmetric Biorthogonal Quantum Systems

Details Supersymmetric Biorthogonal Quantum Systems Supersymmetric Biorthogonal Quantum Systems

2006-03-20

arxiv.org/abs/quant-ph/0603170v2

J.Math.Phys.48:092108,2007

Physics

Quantum Physics

Changes are made to conform to the published version. In particular, some errors are corrected on pp 12-13

Scientific paper

10.1063/1.2191367

We discuss supersymmetric biorthogonal systems, with emphasis given to the periodic solutions that occur at spectral singularities of PT symmetric models. For these periodic solutions, the dual functions are associated polynomials that obey inhomogeneous equations. We construct in detail some explicit examples for the supersymmetric pairs of potentials V_{+/-}(z) = -U(z)^2 +/- z(d/(dz))U(z) where U(z) = \sum_{k>0}u_{k}z^{k}. In particular, we consider the cases generated by U(z) = z and z/(1-z). We also briefly consider the effects of magnetic vector potentials on the partition functions of these systems.

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