Quasi-exactly solvable potentials in Wigner-Dunkl quantum mechanics

• URL: http://arxiv.org/abs/2401.04586v2
• Date: Tue, 19 Mar 2024 15:20:03 GMT
• Title: Quasi-exactly solvable potentials in Wigner-Dunkl quantum mechanics
• Authors: C. Quesne,
• Abstract summary: It is shown that the Dunkl harmonic oscillator on the line can be generalized to a quasi-exactly solvable one. The Hamiltonian of the latter can also be rewritten in a simpler way in terms of an extended Dunkl derivative.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: It is shown that the Dunkl harmonic oscillator on the line can be generalized to a quasi-exactly solvable one, which is an anharmonic oscillator with $n+1$ known eigenstates for any $n\in \N$. It is also proved that the Hamiltonian of the latter can also be rewritten in a simpler way in terms of an extended Dunkl derivative. Furthermore, the Dunkl isotropic oscillator and Dunkl Coulomb potentials in the plane are generalized to quasi-exactly solvable ones. In the former case, potentials with $n+1$ known eigenstates are obtained, whereas, in the latter, sets of $n+1$ potentials associated with a given energy are derived.

Related papers

• Pseudo-Hermitian extensions of the harmonic and isotonic oscillators [9.944647907864256]
  We describe certain pseudo-Hermitian extensions of the harmonic and isotonic oscillators. We explicitly solve for the wavefunctions in the position representation and also explore their intertwining relations.
  arXiv  Detail & Related papers  (2024-08-02T17:15:17Z)
• Energetics of the dissipative quantum oscillator [22.76327908349951]
  We discuss some aspects of the energetics of a quantum Brownian particle placed in a harmonic trap. Based on the fluctuation-dissipation theorem, we analyze two distinct notions of thermally-averaged energy. We generalize our analysis to the case of the three-dimensional dissipative magneto-oscillator.
  arXiv  Detail & Related papers  (2023-10-05T15:18:56Z)
• 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)
• The bound-state solutions of the one-dimensional pseudoharmonic oscillator [0.0]
  We study the bound states of a quantum mechanical system governed by a constant $alpha$. For attractive potentials within the range $-1/4leqalpha0$, there is an even-parity ground state with increasingly negative energy. We show how the regularized excited states approach their unregularized counterparts.
  arXiv  Detail & Related papers  (2021-11-24T23:03:10Z)
• From quartic anharmonic oscillator to double well potential [77.34726150561087]
  It is shown that by taking uniformly-accurate approximation for anharmonic oscillator eigenfunction $Psi_ao(u)$, obtained recently, it is possible to get highly accurate approximation for both the eigenfunctions of the double-well potential and its eigenvalues.
  arXiv  Detail & Related papers  (2021-10-30T20:16:27Z)
• Generalized semiconfined harmonic oscillator model with a position-dependent effective mas [0.0]
  It is shown that a semiconfined harmonic oscillator model with a position-dependent mass in the BenDaniel-Duke setting can be easily constructed. A further generalization is proposed by considering a $m$-dependent position-dependent mass for $0m2$ and deriving the associated semiconfined potential. The potential that would result from a general von Roos kinetic energy operator is presented and the examples of the Zhu-Kroemer and Mustafa-Mazharimousavi settings are briefly discussed.
  arXiv  Detail & Related papers  (2021-10-20T14:23:53Z)
• Linear growth of the entanglement entropy for quadratic Hamiltonians and arbitrary initial states [11.04121146441257]
  We prove that the entanglement entropy of any pure initial state of a bosonic quantum system grows linearly in time. We discuss several applications of our results to physical systems with (weakly) interacting Hamiltonians and periodically driven quantum systems.
  arXiv  Detail & Related papers  (2021-07-23T07:55:38Z)
• Bernstein-Greene-Kruskal approach for the quantum Vlasov equation [91.3755431537592]
  The one-dimensional stationary quantum Vlasov equation is analyzed using the energy as one of the dynamical variables. In the semiclassical case where quantum tunneling effects are small, an infinite series solution is developed.
  arXiv  Detail & Related papers  (2021-02-18T20:55:04Z)
• Anharmonic oscillator: a solution [77.34726150561087]
  The dynamics in $x$-space and in $(gx)-space corresponds to the same energy spectrum with effective coupling constant $hbar g2$. A 2-classical generalization leads to a uniform approximation of the wavefunction in $x$-space with unprecedented accuracy.
  arXiv  Detail & Related papers  (2020-11-29T22:13:08Z)
• The Intersection between Dual Potential and SL(2) Algebraic Spectral Problems [0.0]
  The relation between certain Hamiltonians, known as dual, or partner Hamiltonians, under the transformation $xrightbarxbaralpha$ has long been used as a method of simplifying spectral problems in quantum mechanics. It may be possible to construct part of a Hamiltonian's spectrum from the quasi-solvability of its partner Hamiltonian.
  arXiv  Detail & Related papers  (2020-08-21T21:59:43Z)
• The Birman-Schwinger Operator for a Parabolic Quantum Well in a Zero-Thickness Layer in the Presence of a Two-Dimensional Attractive Gaussian Impurity [3.1643632234649486]
  We consider a quantum mechanical particle moving inside an infinitesimally thin layer constrained by a parabolic well in the $x$-direction. We investigate the Birman-Schwinger operator associated to a model assuming the presence of a Gaussian impurity inside the layer. We construct the corresponding self-adjoint Hamiltonian and prove that it is the limit in the norm resolvent sense of a sequence of corresponding Hamiltonians.
  arXiv  Detail & Related papers  (2020-05-20T19:59:11Z)

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.