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arXiv · 1205.5860

Quasi-Hermitian Hamiltonians associated with exceptional orthogonal polynomials

Bikashkali Midya
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Abstract

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- or 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.

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BibTeXRIS

Bikashkali Midya. 2012-05-26. Quasi-Hermitian Hamiltonians associated with exceptional orthogonal polynomials. https://doi.org/10.1016/j.physleta.2012.08.016

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