Investigation of the Dunkl-Schr\"odinger equation for Position Dependent Mass in the presence of a Lie algebraic approach

• URL: http://arxiv.org/abs/2208.12416v1
• Date: Fri, 26 Aug 2022 03:13:31 GMT
• Title: Investigation of the Dunkl-Schr\"odinger equation for Position Dependent Mass in the presence of a Lie algebraic approach
• Authors: P. Sedaghatnia, H. Hassanabadi, W.S. Chung, B. C. L\"utf\"uo\u{g}lu, S. Hassanabadi and J. K\v{r}\'i\v{z}
• Abstract summary: We formulate the Dunkl-Schr"odinger equation within the position-dependent mass formalism. Our systematic approach lets us observe some new findings in addition to the earlier ones.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Recent studies have shown that the use of Dunkl derivatives instead of ordinary derivatives leads to deriving parity-dependent dynamic solutions. According to this motivation in this manuscript, we formulate the Dunkl-Schr\"odinger equation within the position-dependent mass formalism and derive an algebraic solution out of it. Our systematic approach lets us observe some new findings in addition to the earlier ones. For example, we find that the solution of the Dunkl-Schr\"oodinger equation with position-dependent mass cannot be considered independent of the choice of parameters. Similarly, through the sl(2) algebra, the energy spectrum and the corresponding wave functions are derived in terms of possible Dunkl, ($\mu$), and mass, ($\alpha$), parameters.

Related papers

• Energy transport in a free Euler-Bernoulli beam in terms of Schrödinger's wave function [0.0]
  The dynamics of a free infinite Euler-Bernoulli beam can be described by the Schr"odinger equation for a free particle and vice versa. For two corresponding solutions $u$ and $psi$ the mechanical energy density calculated for $u$ propagates in the beam exactly in the same way as the probability density calculated for $psi$.
  arXiv  Detail & Related papers  (2024-11-06T16:32:11Z)
• 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)
• Time-Dependent Dunkl-Schrödinger Equation with an Angular-Dependent Potential [0.0]
  The Schr"odinger equation is a fundamental equation in quantum mechanics. Over the past decade, theoretical studies have focused on adapting the Dunkl derivative to quantum mechanical problems.
  arXiv  Detail & Related papers  (2024-08-04T13:11:52Z)
• Exact dynamics of quantum dissipative $XX$ models: Wannier-Stark localization in the fragmented operator space [49.1574468325115]
  We find an exceptional point at a critical dissipation strength that separates oscillating and non-oscillating decay. We also describe a different type of dissipation that leads to a single decay mode in the whole operator subspace.
  arXiv  Detail & Related papers  (2024-05-27T16:11:39Z)
• Free expansion of a Gaussian wavepacket using operator manipulations [77.34726150561087]
  The free expansion of a Gaussian wavepacket is a problem commonly discussed in undergraduate quantum classes. We provide an alternative way to calculate the free expansion by recognizing that the Gaussian wavepacket can be thought of as the ground state of a harmonic oscillator. As quantum instruction evolves to include more quantum information science applications, reworking this well known problem using a squeezing formalism will help students develop intuition for how squeezed states are used in quantum sensing.
  arXiv  Detail & Related papers  (2023-04-28T19:20:52Z)
• Third quantization of open quantum systems: new dissipative symmetries and connections to phase-space and Keldysh field theory formulations [77.34726150561087]
  We reformulate the technique of third quantization in a way that explicitly connects all three methods. We first show that our formulation reveals a fundamental dissipative symmetry present in all quadratic bosonic or fermionic Lindbladians. For bosons, we then show that the Wigner function and the characteristic function can be thought of as ''wavefunctions'' of the density matrix.
  arXiv  Detail & Related papers  (2023-02-27T18:56:40Z)
• The Franke-Gorini-Kossakowski-Lindblad-Sudarshan (FGKLS) Equation for Two-Dimensional Systems [62.997667081978825]
  Open quantum systems can obey the Franke-Gorini-Kossakowski-Lindblad-Sudarshan (FGKLS) equation. We exhaustively study the case of a Hilbert space dimension of $2$.
  arXiv  Detail & Related papers  (2022-04-16T07:03:54Z)
• Analytical solutions of the one-dimensional Schr\"{o}dinger equation with position-dependent mass [0.0]
  The study of the Schr"odinger equation with the position-dependent effective mass has attracted a lot of attention. In the present work we obtain several classes of solutions of the one-dimensional Schr"odinger equation with position-dependent particle mass.
  arXiv  Detail & Related papers  (2021-03-19T10:28:06Z)
• 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)
• New approach to describe two coupled spins in a variable magnetic field [55.41644538483948]
  We describe the evolution of two spins coupled by hyperfine interaction in an external time-dependent magnetic field. We modify the time-dependent Schr"odinger equation through a change of representation. The solution is highly simplified when an adiabatically varying magnetic field perturbs the system.
  arXiv  Detail & Related papers  (2020-11-23T17:29:31Z)

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.