Effect of the two-parameter generalized Dunkl derivative on the
two-dimensional Schr\"odinger equation
- URL: http://arxiv.org/abs/2207.10048v2
- Date: Tue, 26 Jul 2022 16:22:27 GMT
- Title: Effect of the two-parameter generalized Dunkl derivative on the
two-dimensional Schr\"odinger equation
- Authors: R.D. Mota, D. Ojeda-Guill\'en
- Abstract summary: 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.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: 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. The eigenfunctions and the energy spectrum for the harmonic
oscillator and the Coulomb problem are derived in an analytical way and it is
shown that our results are properly reduced to those previously reported for
the Dunkl derivative with a single parameter.
Related papers
- Quantum simulation of the Fokker-Planck equation via Schrodingerization [33.76659022113328]
This paper studies a quantum simulation technique for solving the Fokker-Planck equation.
We employ the Schrodingerization method-it converts any linear partial and ordinary differential equation with non-Hermitian dynamics into systems of Schrodinger-type equations.
arXiv Detail & Related papers (2024-04-21T08:53:27Z) - Quantum simulation of partial differential equations via
Schrodingerisation: technical details [31.986350313948435]
We study a new method - called Schrodingerisation introduced in [Jin, Liu, Yu, arXiv: 2212.13969] - for solving general linear partial differential equations with quantum simulation.
This method converts linear partial differential equations into a Schrodingerised' or Hamiltonian system, using a new and simple transformation called the warped phase transformation.
We apply this to more examples of partial differential equations, including heat, convection, Fokker-Planck, linear Boltzmann and Black-Scholes equations.
arXiv Detail & Related papers (2022-12-30T13:47:35Z) - Investigation of the Dunkl-Schr\"odinger equation for Position Dependent
Mass in the presence of a Lie algebraic approach [0.0]
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.
arXiv Detail & Related papers (2022-08-26T03:13:31Z) - Relativistic Solutions of Generalized-Dunkl Harmonic and Anharmonic
Oscillators [0.0]
Dunkl derivative enriches solutions by discussing parity due to its reflection operator.
We show that degenerate states can occur according to the Wigner parameter values.
arXiv Detail & Related papers (2022-08-22T17:47:08Z) - Two electrons in harmonic confinement coupled to light in a cavity [62.997667081978825]
The energy and wave function of a harmonically confined two-electron system coupled to light is calculated.
Relative motion wave function has a known quasi-analytical solution.
arXiv Detail & Related papers (2021-08-03T18:56:50Z) - Exact solution of the two-axis two-spin Hamiltonian [13.019528663019488]
Bethe ansatz solution of the two-axis two-spin Hamiltonian is derived based on the Jordan-Schwinger boson realization of the SU(2) algebra.
It is shown that the solution of the Bethe ansatz equations can be obtained as zeros of the related extended Heine-Stieltjess.
arXiv Detail & Related papers (2021-08-02T02:42:43Z) - Entanglement Entropy of Non-Hermitian Free Fermions [59.54862183456067]
We study the entanglement properties of non-Hermitian free fermionic models with translation symmetry.
Our results show that the entanglement entropy has a logarithmic correction to the area law in both one-dimensional and two-dimensional systems.
arXiv Detail & Related papers (2021-05-20T14:46:09Z) - 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 [0.0]
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.
arXiv Detail & Related papers (2021-03-07T21:34:20Z) - 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) - Alternative quantisation condition for wavepacket dynamics in a
hyperbolic double well [0.0]
We propose an analytical approach for computing the eigenspectrum and corresponding eigenstates of a hyperbolic double well potential of arbitrary height or width.
Considering initial wave packets of different widths and peak locations, we compute autocorrelation functions and quasiprobability distributions.
arXiv Detail & Related papers (2020-09-18T10:29:04Z) - Exact Solutions of the 2D Dunkl--Klein--Gordon Equation: The Coulomb
Potential and the Klein--Gordon Oscillator [0.0]
We introduce the Dunkl--Klein--Gordon (DKG) equation in 2D by changing the standard partial derivatives.
We compute the energy spectrum and eigenfunctions of the DKG equations for the 2D Coulomb potential.
We show that if the parameters of the Dunkl derivative vanish, the obtained results suitably reduce to those reported in the literature for these 2D problems.
arXiv Detail & Related papers (2020-08-30T15:53:57Z)
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.