Supersymmetric Quantum Mechanics with Reflections

Abstract

We consider a realization of supersymmetric quantum mechanics where supercharges are differential-difference operators with reflections. A supersymmetric system with an extended Scarf I potential is presented and analyzed. Its eigenfunctions are given in terms of little -1 Jacobi polynomials which obey an eigenvalue equation of Dunkl type and arise as a q-> -1 limit of the little q-Jacobi polynomials. Intertwining operators connecting the wave functions of extended Scarf I potentials with different parameters are presented.

17 pages

References in corpus (3)

• Solvable Rational Potentials and Exceptional Orthogonal Polynomials in Supersymmetric Quantum Mechanics
• From $s{l}_q(2)$ to a Parabosonic Hopf Algebra
• A Bochner Theorem for Dunkl Polynomials

Cited by in corpus (11)

• Rationally-extended Dunkl oscillator on the line
• Ground-state isolation and discrete flows in a rationally extended quantum harmonic oscillator
• An infinite family of superintegrable Hamiltonians with reflection in the plane
• Jordan algebras and orthogonal polynomials
• Deformed su(1,1) Algebra as a Model for Quantum Oscillators
• Non-Hermitian Oscillator and R-deformed Heisenberg Algebra
• Two-step asymptotics of scaled Dunkl processes
• N-fold Supersymmetric Quantum Mechanics with Reflections
• Non-Hermitian inverted Harmonic Oscillator-Type Hamiltonians Generated from Supersymmetry with Reflections
• Supersymmetric Quantum Mechanics, Engineered Hierarchies of Integrable Potentials, and the Generalised Laguerre Polynomials
• Fractional supersymmetry algebra and lacunary Hermite polynomials