May 2012
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Quasi-Hermitian Hamiltonians associated with exceptional orthogonal polynomials

Bikashkali Midya

Using the method of point canonical transformation, we derive some exactly solvable rationally extended quantum Hamiltonians which are non-Hermitian in nature and whose bound state wave functions are associated with Laguerre and Jacobi-type $$X_1$$ exceptional orthogonal polynomials. These Hamiltonians are shown, with the help of imaginary shift of co-ordinate: $$e^{-\alpha p} x e^{\alpha p} = x+ i \alpha$$, to be both quasi and pseudo-Hermitian. It turns out that the corresponding energy spectra is entirely real.

http://arxiv.org/abs/1205.5860
Mathematical Physics (math-ph); Quantum Physics (quant-ph)