Exact solutions of the Schr\"odinger Equation with Dunkl Derivative for the Free-Particle Spherical Waves, the Pseudo-Harmonic Oscillator and the Mie-type Potential

• URL: http://arxiv.org/abs/2103.04461v1
• Date: Sun, 7 Mar 2021 21:34:20 GMT
• Title: Exact solutions of the Schr\"odinger Equation with Dunkl Derivative for the Free-Particle Spherical Waves, the Pseudo-Harmonic Oscillator and the Mie-type Potential
• Authors: R. D. Mota and D. Ojeda-Guill\'en
• Abstract summary: The equations for the radial and angular parts are obtained by using spherical coordinates and separation of variables. It is shown that our results are adequately reduced to those previously reported when we remove the Dunkl derivative parameters.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We solve exactly the Schr\"odinger equation for the free-particle, the pseudo-harmonic oscillator and the Mie-type potential in three dimensions with the Dunkl derivative. The equations for the radial and angular parts are obtained by using spherical coordinates and separation of variables. The wave functions and the energy spectrum for these potentials are derived in an analytical way and it is shown that our results are adequately reduced to those previously reported when we remove the Dunkl derivative parameters.

Related papers

• Dunkl-Klein-Gordon Equation in Higher Dimensions [0.0]
  We replace the standard partial derivatives in the Klein-Gordon equation with Dunkl derivatives. We obtain exact analytical solutions for the eigenvalues and eigenfunctions of the Dunkl-Klein-Gordon equation in higher dimensions.
  arXiv  Detail & Related papers  (2024-09-19T11:10:12Z)
• Dunkl-Schrodinger Equation in Higher Dimension [0.0]
  This paper presents analytical solutions for eigenvalues and eigenfunctions of the Schr"odinger equation in higher dimensions. Two fundamental quantum mechanical problems are examined in their exact forms. The behavior of the energy eigenvalue functions are illustrated graphically with the reduced probability densities.
  arXiv  Detail & Related papers  (2024-09-19T11:03:25Z)
• Leading correction to the relativistic Foldy-Wouthuysen Hamiltonian [55.2480439325792]
  We rigorously derive a leading correction in the weak-field approximation to the known relativistic Foldy-Wouthuysen Hamiltonian. For Dirac particles, the relativistic wave equation of the second order is obtained with the correction similar to that to the Foldy-Wouthuysen Hamiltonian.
  arXiv  Detail & Related papers  (2024-08-03T12:53:41Z)
• Dunkl-Schrödinger equation with time-dependent harmonic oscillator potential [0.0]
  We determine the explicit form of the wavefunctions of one- and three-dimensional harmonic oscillators with time-dependent mass and frequency. We derivation a parity-dependent of the invariant and auxiliary equation.
  arXiv  Detail & Related papers  (2024-07-11T14:18:24Z)
• Tunneling dynamics of the relativistic Schrödinger/Salpeter equation [0.0]
  We investigate potential scattering and tunneling dynamics of a particle wavepacket evolving according to the Salpeter equation. The tunneling properties of the Salpeter equation differ from those of the standard relativistic wave equations. The solutions are characterized by the absence of Klein tunneling and an effect of the potential on the fraction of the transmitted wavepacket that propagates outside the light cone.
  arXiv  Detail & Related papers  (2024-06-24T13:49:34Z)
• Double-scale theory [77.34726150561087]
  We present a new interpretation of quantum mechanics, called the double-scale theory. It is based on the simultaneous existence of two wave functions in the laboratory reference frame. The external wave function corresponds to a field that pilots the center-of-mass of the quantum system. The internal wave function corresponds to the interpretation proposed by Edwin Schr"odinger.
  arXiv  Detail & Related papers  (2023-05-29T14:28:31Z)
• On the Su-Schrieffer-Heeger model of electron transport: low-temperature optical conductivity by the Mellin transform [62.997667081978825]
  We describe the low-temperature optical conductivity as a function of frequency for a quantum-mechanical system of electrons that hop along a polymer chain. Our goal is to show vias how the interband conductivity of this system behaves as the smallest energy bandgap tends to close.
  arXiv  Detail & Related papers  (2022-09-26T23:17:39Z)
• Effect of the two-parameter generalized Dunkl derivative on the two-dimensional Schr\"odinger equation [0.0]
  We introduce a generalization of the Dunkl-derivative with two parameters to study the Schr"odinger equation in Cartesian and polar coordinates in two dimensions.
  arXiv  Detail & Related papers  (2022-07-20T17:27:08Z)
• Machine Learning S-Wave Scattering Phase Shifts Bypassing the Radial Schr\"odinger Equation [77.34726150561087]
  We present a proof of concept machine learning model resting on a convolutional neural network capable to yield accurate scattering s-wave phase shifts. We discuss how the Hamiltonian can serve as a guiding principle in the construction of a physically-motivated descriptor.
  arXiv  Detail & Related papers  (2021-06-25T17:25:38Z)
• $\mathcal{P}$,$\mathcal{T}$-odd effects for RaOH molecule in the excited vibrational state [77.34726150561087]
  Triatomic molecule RaOH combines the advantages of laser-coolability and the spectrum with close opposite-parity doublets. We obtain the rovibrational wave functions of RaOH in the ground electronic state and excited vibrational state using the close-coupled equations derived from the adiabatic Hamiltonian.
  arXiv  Detail & Related papers  (2020-12-15T17:08:33Z)
• Shape of a sound wave in a weakly-perturbed Bose gas [23.87373187143897]
  We study acoustic emission generated in a uniform Bose gas by a static impurity. The impurity excites a sound-wave packet, which propagates through the gas. We calculate the shape of this wave packet in the limit of long wave lengths.
  arXiv  Detail & Related papers  (2020-04-17T06:19:29Z)

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.