Quasi-Hermitian Hamiltonians associated with exceptional orthogonal polynomials

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 X1 exceptional orthogonal polynomials. These Hamiltonians are shown, with the help of imaginary shift of coordinate: e−αpxeαp=x+iα, to be both quasi- and pseudo-Hermitian. It turns out that the corresponding energy spectra is entirely real.