December 2014
Mon Tue Wed Thu Fri Sat Sun
« Nov    
1234567
891011121314
15161718192021
22232425262728
293031  

Day December 9, 2014

A new non-Hermitian \(E_2\)-quasi-exactly solvable model

Andreas Fring

We construct a previously unknown \(E_2\)-quasi-exactly solvable non-Hermitian model whose eigenfunctions involve weakly orthogonal polynomials obeying three-term recurrence relations that factorize beyond the quantization level. The model becomes Hermitian when one of its two parameters is fixed to a specific value. We analyze the double scaling limit of this model leading to the complex Mathieu equation. The norms, Stieltjes measures and moment functionals are evaluated for some concrete values of one of the two parameters.

http://arxiv.org/abs/1412.2800
Quantum Physics (quant-ph); Mathematical Physics (math-ph)