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 $X_1$ 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.

References in corpus (8)

• Making Sense of Non-Hermitian Hamiltonians
• Infinitely many shape invariant potentials and new orthogonal polynomials
• Exceptional orthogonal polynomials, exactly solvable potentials and supersymmetry
• Solvable rational extensions of the isotonic oscillator
• Exceptional orthogonal polynomials and the Darboux transformation
• Construction of a unique metric in quasi-Hermitian quantum mechanics: non-existence of the charge operator in a 2 x 2 matrix model
• Dirac(-Pauli), Fokker-Planck equations and exceptional Laguerre polynomials
• Effect of Position-dependent Mass on Dynamical Breaking of Type B and Type X_2 N-fold Supersymmetry

Cited by in corpus (1)

• Infinite families of (non)-Hermitian Hamiltonians associated with exceptional $X_m$ Jacobi polynomials