Rationally-extended Dunkl oscillator on the line

Abstract It is shown that the extensions of exactly-solvable quantum mechanical problems connected with replacement ordinary derivatives by Dunkl ones and classical orthogonal polynomials exceptional can be easily combined. For such a purpose, example oscillator on line considered three different types rationally-extended oscillators are constructed. The corresponding wavefunctions expressed in terms generalized Hermite polynomials, defined X m -Laguerre polynomials. Furthermore, extended Hamiltonians to expressible some anharmonic potentials.