One-dimensional Dunkl Quantum Mechanics: A Path Integral Approach

• URL: http://arxiv.org/abs/2407.12644v1
• Date: Wed, 17 Jul 2024 15:14:44 GMT
• Title: One-dimensional Dunkl Quantum Mechanics: A Path Integral Approach
• Authors: A. Benchikha, B. Hamil, B. C. Lütfüoğlu, B. Khantoul,
• Abstract summary: We derive the propagator in one-dimensional Wigner-Dunkl quantum mechanics. We deduce the energy spectra and the corresponding bound-state wave functions from the spectral decomposition of the propagator.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In the present manuscript, we employ the Feynman path integral method to derive the propagator in one-dimensional Wigner-Dunkl quantum mechanics. To verify our findings we calculate the propagator associated with the free particle and the harmonic oscillator in the presence of the Dunkl derivative. We also deduce the energy spectra and the corresponding bound-state wave functions from the spectral decomposition of the propagator.

Related papers

• Interpretation of wave function by coherent ensembles of trajectories [0.0]
  We revise the ensemble interpretation of wave function in quantum mechanics. We introduce coherence (auto-concordance) of ensembles of quantum trajectories in the space-time.
  arXiv  Detail & Related papers  (2024-07-12T14:10:04Z)
• On the Path Integral Formulation of Wigner-Dunkl Quantum Mechanics [0.0]
  Feynman's path integral approach is studied in the framework of the Wigner-Dunkl deformation of quantum mechanics. We look at the Euclidean time evolution and the related Dunkl process.
  arXiv  Detail & Related papers  (2023-12-20T10:23:34Z)
• Free particle trapped in an infinite quantum well examined through the discrete calculus model [0.0]
  We use the discrete approach to solve the Schr"odinger equations for a free particle and the quantum gas of free particles embedded in an infinite quantum well with the finite width. We obtain the expressions of energy eigenvalues, the eigenfunctions as well as the density matrix and partition function for the discrete case.
  arXiv  Detail & Related papers  (2023-03-14T20:10:18Z)
• Lorentzian path integral for quantum tunneling and WKB approximation for wave-function [0.0]
  We show that the Picard-Lefschetz Lorentzian formulation is consistent with the WKB approximation for wave-function. We discuss a simpler semiclassical approximation of the Lorentzian path integral without integrating the lapse function.
  arXiv  Detail & Related papers  (2021-02-19T07:00:01Z)
• 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)
• Quantum particle across Grushin singularity [77.34726150561087]
  We study the phenomenon of transmission across the singularity that separates the two half-cylinders. All the local realisations of the free (Laplace-Beltrami) quantum Hamiltonian are examined as non-equivalent protocols of transmission/reflection. This allows to comprehend the distinguished status of the so-called bridging' transmission protocol previously identified in the literature.
  arXiv  Detail & Related papers  (2020-11-27T12:53:23Z)
• Feynman Functional Integral in the Fokker Theory [62.997667081978825]
  equivalence of two formulations of Fokker's quantum theory is proved. The common basis for the two approaches is the generalized canonical form of Fokker's action.
  arXiv  Detail & Related papers  (2020-11-11T12:10:01Z)
• Theory of waveguide-QED with moving emitters [68.8204255655161]
  We study a system composed by a waveguide and a moving quantum emitter in the single excitation subspace. We first characterize single-photon scattering off a single moving quantum emitter, showing both nonreciprocal transmission and recoil-induced reduction of the quantum emitter motional energy.
  arXiv  Detail & Related papers  (2020-03-20T12:14:10Z)
• Feynman Propagator for a System of Interacting Scalar Particles in the Fokker Theory [62.997667081978825]
  The functional integral on the generalized phase space is defined as the initial one in quantum theory. The measure of integration in the generalized configuration space of world particle lines is determined. A modification of the propagator is proposed, in which the role of independent time parameters is taken by the time coordinates of the particles in Minkowski space.
  arXiv  Detail & Related papers  (2020-02-10T09:09:45Z)
• From stochastic spin chains to quantum Kardar-Parisi-Zhang dynamics [68.8204255655161]
  We introduce the asymmetric extension of the Quantum Symmetric Simple Exclusion Process. We show that the time-integrated current of fermions defines a height field which exhibits a quantum non-linear dynamics.
  arXiv  Detail & Related papers  (2020-01-13T14:30:36Z)

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.