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 co-ordinate: e−αpxeαp=x+iα, to be both quasi and pseudo-Hermitian. It turns
out that the corresponding energy spectra is entirely real