Approximate solutions of the Schrodinger equation with Hulthen-Hellmann Potentials for a Quarkonium system

• URL: http://arxiv.org/abs/2101.01175v1
• Date: Sat, 2 Jan 2021 00:02:41 GMT
• Title: Approximate solutions of the Schrodinger equation with Hulthen-Hellmann Potentials for a Quarkonium system
• Authors: I. O. Akpan, E. P. Inyang, E. P. Inyang and E. S. William
• Abstract summary: Hulth'en plus Hellmann potentials are adopted as the quark-antiquark interaction potential. Four special cases were considered when some of the potential parameters were set to zero.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Hulth\'en plus Hellmann potentials are adopted as the quark-antiquark interaction potential for studying the mass spectra of heavy mesons. We solved the radial Schr\"odinger equation analytically using the Nikiforov-Uvarov method. The energy eigenvalues and corresponding wave function in terms of Laguerre polynomials were obtained. The present results are applied for calculating the mass of heavy mesons such as charmonium and bottomonium . Four special cases were considered when some of the potential parameters were set to zero, resulting into Hellmann potential, Yukawa potential, Coulomb potential, and Hulth\'en potential, respectively. The present potential provides satisfying results in comparison with experimental data and the work of other researchers.

Related papers

• Ultracold Neutrons in the Low Curvature Limit: Remarks on the post-Newtonian effects [49.1574468325115]
  We apply a perturbative scheme to derive the non-relativistic Schr"odinger equation in curved spacetime. We calculate the next-to-leading order corrections to the neutron's energy spectrum. While the current precision for observations of ultracold neutrons may not yet enable to probe them, they could still be relevant in the future or in alternative circumstances.
  arXiv  Detail & Related papers  (2023-12-30T16:45:56Z)
• Independent-oscillator model and the quantum Langevin equation for an oscillator: A review [19.372542786476803]
  A derivation of the quantum Langevin equation is outlined based on the microscopic model of the heat bath. In the steady state, we analyze the quantum counterpart of energy equipartition theorem. The free energy, entropy, specific heat, and third law of thermodynamics are discussed for one-dimensional quantum Brownian motion.
  arXiv  Detail & Related papers  (2023-06-05T07:59:35Z)
• Thermal masses and trapped-ion quantum spin models: a self-consistent approach to Yukawa-type interactions in the $λ\!φ^4$ model [44.99833362998488]
  A quantum simulation of magnetism in trapped-ion systems makes use of the crystal vibrations to mediate pairwise interactions between spins. These interactions can be accounted for by a long-wavelength relativistic theory, where the phonons are described by a coarse-grained Klein-Gordon field. We show that thermal effects, which can be controlled by laser cooling, can unveil this flow through the appearance of thermal masses in interacting QFTs.
  arXiv  Detail & Related papers  (2023-05-10T12:59:07Z)
• Application of Eckart-Hellmann potential to study selected diatomic molecules using Nikiforov-Uvarov-Functional Analysis (NUFA) method [0.0]
  We study the energy levels of the Schr"odinger equation under the Eckart-Hellmann potential (EHP) energy function. The numerical bound states energy for various screening parameters at different quantum states and vibrational energies of EHP for CuLi, TiH, VH, and TiC diatomic molecules were computed.
  arXiv  Detail & Related papers  (2022-04-08T19:24:43Z)
• Approximate Solutions, Thermal Properties and Superstatistics Solutions to Schr\"odinger Equation [0.0]
  We study thermal properties and superstatistics in terms of partition function (Z) and other thermodynamic properties. The proposed potential model reduces to Hellmann potential, Yukawa potential, Screened Hyperbolic potential and Coulomb potential as special cases.
  arXiv  Detail & Related papers  (2021-10-16T22:02:50Z)
• When can a local Hamiltonian be recovered from a steady state? [11.031662961887243]
  Hamiltonians of two spin chains with 2-local interactions and 3-local interactions can be recovered by measuring local observables. We show that when the chain length reaches a certain critical number, we can recover the local Hamiltonian from its one steady state by solving the homogeneous operator equation (HOE) To explain the existence of such a critical chain length, we develop an alternative method to recover Hamiltonian by solving the energy eigenvalue equations (EEE)
  arXiv  Detail & Related papers  (2021-09-16T02:37:17Z)
• 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)
• 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)
• Study on the applicability of Varshni potential to predict the mass-spectra of the quark-antiquark systems in a non-relativistic framework [0.0]
  We obtain the Schr"odinger equation for the Varshni potential using the Nikiforov-Uvarov method. The corresponding eigenfunction is obtained in terms of Laguerres and spectra. We applied the present results to calculate heavy-meson masses of charmonium and bottomonium.
  arXiv  Detail & Related papers  (2021-01-01T23:24:12Z)
• Analytical Investigation of Meson Spectrum via Exact Quantization Rule Approach [0.0]
  We solve the radial Schr"odinger equation analytically using the Exact Quantization Rule approach to obtain the energy eigenvalues with the Extended Cornell potential ECP. The present potential provides excellent results in comparison with experimental data with a maximum error of 0.0065 GeV and work of other researchers.
  arXiv  Detail & Related papers  (2020-12-19T09:40:26Z)
• $\mathcal{P}$,$\mathcal{T}$-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)

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.