Solutions of the scattering problem in a complete set of Bessel functions with a discrete index

• URL: http://arxiv.org/abs/2209.03738v1
• Date: Wed, 7 Sep 2022 01:22:48 GMT
• Title: Solutions of the scattering problem in a complete set of Bessel functions with a discrete index
• Authors: A. D. Alhaidari and M. E. H. Ismail
• Abstract summary: We use the tridiagonal representation approach to solve the radial Schr"odinger equation for the continuum scattering states of the Kratzer potential. We do the same for a radial power-law potential with inverse-square and inverse-cube singularities.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We use the tridiagonal representation approach to solve the radial Schr\"odinger equation for the continuum scattering states of the Kratzer potential. We do the same for a radial power-law potential with inverse-square and inverse-cube singularities. These solutions are written as infinite convergent series of Bessel functions with a discrete index. As physical application of the latter solution, we treat electron scattering off a neutral molecule with electric dipole and electric quadrupole moments.

Related papers

• Dynamics of discrete solitons in the fractional discrete nonlinear Schrödinger equation with the quasi-Riesz derivative [11.705651144832041]
  This equation represents a novel discrete system in which the nearest-neighbor coupling is combined with long-range interactions. The dispersion relation for lattice waves and the corresponding propagation band in the system's linear spectrum are found in an exact form for all values of LI. Formation of single-site and two-site discrete solitons is explored, starting from the anti-continuum limit. Mobility of the discrete solitons is considered too, by means of an estimate of the system's Peierls-Nabarro potential barrier.
  arXiv  Detail & Related papers  (2024-07-17T09:52:18Z)
• 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)
• Neural Pfaffians: Solving Many Many-Electron Schrödinger Equations [58.130170155147205]
  Neural wave functions accomplished unprecedented accuracies in approximating the ground state of many-electron systems, though at a high computational cost. Recent works proposed amortizing the cost by learning generalized wave functions across different structures and compounds instead of solving each problem independently. This work tackles the problem by defining overparametrized, fully learnable neural wave functions suitable for generalization across molecules.
  arXiv  Detail & Related papers  (2024-05-23T16:30:51Z)
• Finite-element assembly approach of optical quantum walk networks [39.58317527488534]
  We present a finite-element approach for computing the aggregate scattering matrix of a network of linear coherent scatterers. Unlike traditional finite-element methods in optics, this method does not directly solve Maxwell's equations.
  arXiv  Detail & Related papers  (2024-05-14T18:04:25Z)
• Relativistic exponential-type spinor orbitals and their use in many-electron Dirac equation solution [0.0]
  Dirac-Coulomb type differential equation and its solution relativistic exponential-type spinor orbitals are introduced. A new formulation for relativistic auxiliary functions that improve the efficiency in Coulomb energy calculations is presented.
  arXiv  Detail & Related papers  (2024-03-23T20:48:54Z)
• Dissipatons as generalized Brownian particles for open quantum systems: Dissipaton-embedded quantum master equation [14.746754599760562]
  We revisit the dissipaton equation of motion theory and establish an equivalent dissipatons-embedded quantum master equation (DQME) The DQME supplies a direct approach to investigate the statistical characteristics of dissipatons and thus the physically supporting hybrid bath modes. Numerical demonstrations are carried out on the electron transfer model, exhibiting the transient statistical properties of the solvation coordinate.
  arXiv  Detail & Related papers  (2023-03-19T14:14:46Z)
• Electron scattering of mass-inverted in graphene quantum dots [0.0]
  We study the scattering of Dirac electrons of circular graphene quantum dot with mass-inverted subject to electrostatic potential. It is found that the presence of a mass term outside in addition to another one inside the quantum dot strongly affects the scattering of electrons.
  arXiv  Detail & Related papers  (2022-02-25T18:37:26Z)
• 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)
• Functional integral method for potential scattering amplitude in quantum mechanics [0.0]
  We will obtain the potential scattering amplitude form the complete Green function in the corresponding external field through solving the Schrodinger equation. Consider specific external potentials such as the Yukawa or Gaussian potential, we will find the corresponding differential scattering cross-sections.
  arXiv  Detail & Related papers  (2021-04-02T01:16:51Z)
• Dynamical formulation of low-energy scattering in one dimension [0.0]
  A transfer matrix $mathbfM$ of a short-range potential may be expressed in terms of the time-evolution operator for an effective two-level quantum system. We explore the utility of this formulation in the study of the low-energy behavior of the scattering data.
  arXiv  Detail & Related papers  (2021-02-11T15:55:34Z)
• Confinement in Gapped Graphene with Magnetic Flux [0.0]
  We study the propagation of electrons in a circular quantum dot of gapped graphene subject to the magnetic flux $phi$. We identify different scattering regimes as a function of the physical parameters such as the incident electronic energy, potential barrier, radius of quantum dot, gap and $phi$.
  arXiv  Detail & Related papers  (2020-06-13T12:17:30Z)

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.