Fring, A. (2015). E2quasiexact solvability for nonHermitian models. Journal of Physics A: Mathematical and General, 48(14), pp. 145301145320. doi: 10.1088/17518113/48/14/145301

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Abstract
We propose the notion of E2quasiexact solvability and apply this idea to find explicit solutions to the eigenvalue problem for a nonHermitian Hamiltonian system depending on two parameters. The model considered reduces to the complex Mathieu Hamiltonian in a double scaling limit, which enables us to compute the exceptional points in the energy spectrum of the latter as a limiting process of the zeros for some algebraic equations. The coefficient functions in the quasiexact eigenfunctions are univariate polynomials in the energy obeying a threeterm recurrence relation. The latter property guarantees the existence of a linear functional such that the polynomials become orthogonal. The polynomials are shown to factorize for all levels above the quantization condition leading to vanishing norms rendering them to be weakly orthogonal. In two concrete examples we compute the explicit expressions for the Stieltjes measure.
Item Type:  Article 

Subjects:  Q Science > QA Mathematics 
Divisions:  School of Engineering & Mathematical Sciences > Department of Mathematical Science 
URI:  http://openaccess.city.ac.uk/id/eprint/7579 
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