The Fractional Schrodinger Equation with the Generalized Woods-Saxon Potential

• URL: http://arxiv.org/abs/2302.03060v1
• Date: Fri, 20 Jan 2023 10:14:54 GMT
• Title: The Fractional Schrodinger Equation with the Generalized Woods-Saxon Potential
• Authors: M. Abu-Shady and Etido P. Inyang
• Abstract summary: The bound state energy eigenvalues and the corresponding eigenfunctions of the generalized Woods-Saxon potential are studied. Results play important role in molecular chemistry and nuclear physics.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The bound state energy eigenvalues and the corresponding eigenfunctions of the generalized Woods-Saxon potential reported in [Phys. Rev. C 72, 027001 (2005)] is extended to the fractional forms using the generalized fractional derivative and the fractional Nikiforov-Uvarov (NU) technique. Analytical solutions of bound states of the Schrodinger equation for the present potential are obtained in the terms of fractional Jacobi polynomials. It is demonstrated that the classical results are a special case of the present results at Elfa=Beta=1 Therefore, the present results play important role in molecular chemistry and nuclear physics.

Related papers

• Efimov Effect in Long-range Quantum Spin Chains [11.213906010203264]
  We show that the Efimov effect also manifests in long-range quantum spin chains. We theoretically determine how the ratio of two successive binding energies depends on the interaction range. Our results reveal universal physics in dilute quantum gases of magnons that can be experimentally tested in trapped-ion systems.
  arXiv  Detail & Related papers  (2025-02-28T06:28:17Z)
• Bound states of quasiparticles with quartic dispersion in an external potential: WKB approach [0.0]
  The Wentzel-Kramers-Brillouin method is formulated for quasiparticles with quartic-in-momentum dispersion. It is shown that matching wave functions in forbidden and allowed regions requires the consideration of higher-order Airy-type functions.
  arXiv  Detail & Related papers  (2025-02-19T10:50:49Z)
• Generalization of the exact Eriksen and exponential operators of the Foldy-Wouthuysen transformation to arbitrary-spin particles in nonstationary fields [55.2480439325792]
  We use the Foldy-Wouthuysen transformation which allows one to obtain the Schr"odinger picture of relativistic quantum mechanics. Unlike previous publications, we determine exact Eriksen and exponential operators of the Foldy-Wouthuysen transformation.
  arXiv  Detail & Related papers  (2024-10-27T18:41:50Z)
• Dirac Equation Solution with Generalized tanh-Shaped Hyperbolic Potential: Application to Charmonium and Bottomonium Mass Spectra [0.0]
  We use a generalized tanh shaped hyperbolic potential to investigate bound state solutions of the Dirac equation. Results indicate that the energy eigenvalues are strongly correlated with the potential parameters. Using this potential to model mass spectra of charmonium and bottomonium, we show that results for the calculated quark mass spectra align closely with experimentally observed values.
  arXiv  Detail & Related papers  (2024-09-23T20:40:59Z)
• Emergent Liouvillian exceptional points from exact principles [12.084121187559864]
  Liouvillian EPs have been seen in a variety of systems and have been associated to numerous exotic effects. We show that Heisenberg equations for the system exhibit the same EPs as the corresponding master equations.
  arXiv  Detail & Related papers  (2024-09-12T14:53:46Z)
• Bound polariton states in the Dicke-Ising model [41.94295877935867]
  We present a study of hybrid light-matter excitations in cavity QED materials. We derive the exact excitations of the system in the thermodynamic limit.
  arXiv  Detail & Related papers  (2024-06-17T18:00:01Z)
• The Parametric Generalized Fractional Nikiforov-Uvarov Method and Its Applications [0.0]
  The results are applied to the extended Cornell potential, the pesudoharmonic potential, the Mie potential, the Kratzer-Fues potential, the harmonic oscillator potential, the Morse potential, the Woods-Saxon potential, the Hulthen potential, the deformed Rosen-Morse potential and the Poschl-Teller potential.
  arXiv  Detail & Related papers  (2023-01-14T11:10:37Z)
• Quantum Talagrand, KKL and Friedgut's theorems and the learnability of quantum Boolean functions [9.428671399402553]
  We extend three related results from the analysis of influences of Boolean functions to the quantum inequality setting. Our results are derived by a joint use of recently studied hypercontractivity and gradient estimates. We comment on the implications of our results as regards to noncommutative extensions of isoperimetric type inequalities, quantum circuit complexity lower bounds and the learnability of quantum observables.
  arXiv  Detail & Related papers  (2022-09-15T13:12:32Z)
• Non-Relativistic Particle under the Influence of Aharonov-Bohm Flux Field Subject to Physical Potentials and the Nikiforov-Uvarov Method [0.0]
  We investigate the non-relativistic wave equation via the Schr"odinger wave equation under the influence of the Aharonov-Bohm flux field. We obtain the energy profiles and the wave function of the non-relativistic particle, and analyze the effects of potential and the quantum flux on them.
  arXiv  Detail & Related papers  (2022-08-04T04:39:43Z)
• Correspondence Between the Energy Equipartition Theorem in Classical Mechanics and its Phase-Space Formulation in Quantum Mechanics [62.997667081978825]
  In quantum mechanics, the energy per degree of freedom is not equally distributed. We show that in the high-temperature regime, the classical result is recovered.
  arXiv  Detail & Related papers  (2022-05-24T20:51:03Z)
• Out-of-equilibrium dynamics of the Kitaev model on the Bethe lattice via coupled Heisenberg equations [23.87373187143897]
  We study the isotropic Kitaev spin-$1/2$ model on the Bethe lattice. We take a straightforward approach of solving Heisenberg equations for a tailored subset of spin operators. As an example, we calculate the time-dependent expectation value of this observable for a factorized translation-invariant.
  arXiv  Detail & Related papers  (2021-10-25T17:37:33Z)
• Linear growth of the entanglement entropy for quadratic Hamiltonians and arbitrary initial states [11.04121146441257]
  We prove that the entanglement entropy of any pure initial state of a bosonic quantum system grows linearly in time. We discuss several applications of our results to physical systems with (weakly) interacting Hamiltonians and periodically driven quantum systems.
  arXiv  Detail & Related papers  (2021-07-23T07:55:38Z)
• Analytical study on the Applicability of Ultra Generalized Exponential Hyperbolic Potential to Predict the Mass Spectra of the Heavy Mesons [0.0]
  We solve the Klein-Gordon equation analytically using the Nikiforov-Uvarov method. The present results are applied for calculating the mass spectra of heavy mesons such as charmonium (cc) and bottomonium (cc) for different states.
  arXiv  Detail & Related papers  (2021-01-16T07:22:13Z)
• Eigensolutions of the N-dimensional Schr\"odinger equation interacting with Varshni-Hulth\'en potential model [0.0]
  Solution of the N-dimensional Schr"odinger equation for the newly proposed Varshni-Hulth'en potential is presented. numerical energy eigenvalues and the corresponding normalized eigenfunctions are obtained in terms of Jacobis.
  arXiv  Detail & Related papers  (2020-12-26T22:54:13Z)

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.