Rational extensions of the Dunkl oscillator in the plane and exceptional orthogonal polynomials

• URL: http://arxiv.org/abs/2305.05476v2
• Date: Tue, 31 Oct 2023 15:04:17 GMT
• Title: Rational extensions of the Dunkl oscillator in the plane and exceptional orthogonal polynomials
• Authors: C. Quesne
• Abstract summary: It is shown that rational extensions of the isotropic Dunkl oscillator in the plane can be obtained by adding some terms. In the latter, it becomes an anisotropic potential, whose explicit form has been found in the simplest case.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: It is shown that rational extensions of the isotropic Dunkl oscillator in the plane can be obtained by adding some terms either to the radial equation or to the angular one obtained in the polar coordinates approach. In the former case, the isotropic harmonic oscillator is replaced by an isotropic anharmonic one, whose wavefunctions are expressed in terms of $X_m$-Laguerre exceptional orthogonal polynomials. In the latter, it becomes an anisotropic potential, whose explicit form has been found in the simplest case associated with $X_1$-Jacobi exceptional orthogonal polynomials.

Related papers

• Rational Extension of Anisotropic Harmonic Oscillator Potentials in Higher Dimensions [2.6171788822864923]
  This paper presents the first-order supersymmetric rational extension of the quantum anisotropic harmonic oscillator (QAHO) in multiple dimensions, including full-line, half-line, and their combinations. The exact solutions are in terms of the exceptionals. The rationally extended potentials are isospectral to the conventional QAHOs.
  arXiv  Detail & Related papers  (2024-11-05T09:53:57Z)
• Chiral Virasoro algebra from a single wavefunction [14.735587711294299]
  When the edge is purely chiral, the Hilbert space of low-energy edge excitations can form a representation of a single Virasoro algebra. We propose a method to systematically extract the generators of the Virasoro algebra from a single ground state wavefunction.
  arXiv  Detail & Related papers  (2024-03-27T09:54:21Z)
• Rational extensions of an oscillator-shaped quantum well potential in a position-dependent mass background [0.0]
  A recently proposed quantum well model associated with a position-dependent mass can be solved by applying a point canonical transformation to the constant-mass Schr"odinger equation for the Scarf I potential. Some more involved position-dependent mass models associated with $X$-Jacobi exceptionals are also considered.
  arXiv  Detail & Related papers  (2023-09-20T14:46:46Z)
• Harmonic Oscillator with a Step and its Isospectral Properties [0.0]
  We investigate the one-dimensional Schr"odinger equation for a harmonic oscillator with a finite jump $a$ at the origin. The solution is constructed by employing the ordinary matching-of-waves technique.
  arXiv  Detail & Related papers  (2023-07-26T15:31:31Z)
• Rationally-extended Dunkl oscillator on the line [0.0]
  It is shown that the extensions of exactly-solvable quantum mechanical problems connected with the replacement of ordinary derivatives by Dunkl ones can be easily combined.
  arXiv  Detail & Related papers  (2023-04-12T13:20:37Z)
• Solutions of (1+1)-dimensional Dirac equation associated with exceptional orthogonal polynomials and the parametric symmetry [7.343280016515051]
  We consider $1+1$-dimensional Dirac equation with rationally extended scalar potentials corresponding to the radial oscillator, the trigonometric Scarf and the hyperbolic Poschl-Teller potentials.
  arXiv  Detail & Related papers  (2022-11-04T16:23:05Z)
• An Equivalence Principle for the Spectrum of Random Inner-Product Kernel Matrices with Polynomial Scalings [21.727073594338297]
  This study is motivated by applications in machine learning and statistics. We establish the weak limit of the empirical distribution of these random matrices in a scaling regime. Our results can be characterized as the free additive convolution between a Marchenko-Pastur law and a semicircle law.
  arXiv  Detail & Related papers  (2022-05-12T18:50:21Z)
• High-order harmonic generations in tilted Weyl semimetals [11.628719393775771]
  Strong noncentrosymmetrical generations in high orders are observed around a single type-II Weyl point, especially at frequency zero. In consideration of dynamical symmetries, type-I and -II Weyl cones also show different selective responses under the circularly polarized light. Using a more realistic model containing two pairs of Weyl points, we demonstrate the paired Weyl points with opposite chirality could suppress the overall even-order generations.
  arXiv  Detail & Related papers  (2022-05-11T12:09:53Z)
• Out-of-equilibrium dynamics of the Kitaev model on the Bethe lattice via coupled Heisenberg equations [23.87373187143897]
  We study the isotropic Kitaev spin-$1/2$ model on the Bethe lattice. We take a straightforward approach of solving Heisenberg equations for a tailored subset of spin operators. As an example, we calculate the time-dependent expectation value of this observable for a factorized translation-invariant.
  arXiv  Detail & Related papers  (2021-10-25T17:37:33Z)
• Fano interference in quantum resonances from angle-resolved elastic scattering [62.997667081978825]
  We show that probing the angular dependence of the cross section allows us to unveil asymmetric Fano profiles in a single channel shape resonance. We observe a shift in the peak of the resonance profile in the elastic collisions between metastable helium and deuterium molecules.
  arXiv  Detail & Related papers  (2021-05-12T20:41:25Z)
• Quasi-symmetry groups and many-body scar dynamics [13.95461883391858]
  In quantum systems, a subspace spanned by degenerate eigenvectors of the Hamiltonian may have higher symmetries than those of the Hamiltonian itself. When the group is a Lie group, an external field coupled to certain generators of the quasi-symmetry group lifts the degeneracy. We provide two related schemes for constructing one-dimensional spin models having on-demand quasi-symmetry groups.
  arXiv  Detail & Related papers  (2020-07-20T18:05:21Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.