Dirac Equation Solution with Generalized tanh-Shaped Hyperbolic Potential: Application to Charmonium and Bottomonium Mass Spectra

• URL: http://arxiv.org/abs/2409.15538v1
• Date: Mon, 23 Sep 2024 20:40:59 GMT
• Title: Dirac Equation Solution with Generalized tanh-Shaped Hyperbolic Potential: Application to Charmonium and Bottomonium Mass Spectra
• Authors: V. H. Badalov, A. I. Ahmadov, E. A. Dadashov, S. V. Badalov,
• Abstract summary: 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this work, we advance the understanding of the fundamental interactions by using a generalized tanh shaped hyperbolic potential to investigate bound state solutions of the Dirac equation. Using the Nikiforov Uvarov method, we derive energy eigenvalues and radial wave functions in various quantum states, with the results expressed in terms of hypergeometric polynomials. The results of our analysis indicate that the energy eigenvalues are strongly correlated with the potential parameters and covered several fundamental potential models used to expose a nontrivial behaviour that occurred within quantum systems. Further, 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, reflecting the veracity and accuracy of the approach. This close correspondence between calculated and experimental spectra highlights this potential model's efficacy in describing heavy quarkonium systems. The insights gained from this study reinforce the applicability of this potential model in quantum mechanics and particle physics and lay a foundation for its extension to other quantum systems, suggesting a feasible avenue for future research.

Related papers

• Coherence generation with Hamiltonians [44.99833362998488]
  We explore methods to generate quantum coherence through unitary evolutions. This quantity is defined as the maximum derivative of coherence that can be achieved by a Hamiltonian. We identify the quantum states that lead to the largest coherence derivative induced by the Hamiltonian.
  arXiv  Detail & Related papers  (2024-02-27T15:06:40Z)
• 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)
• 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)
• Analytical Ground- and Excited-State Gradients for Molecular Electronic Structure Theory from Hybrid Quantum/Classical Methods [0.0]
  We show how the resulting response contributions to the gradient can be evaluated with a quantum effort. We numerically demonstrate the exactness the analytical gradients and discuss the magnitude of the quantum response contributions.
  arXiv  Detail & Related papers  (2021-10-11T07:14:54Z)
• Spectral density reconstruction with Chebyshev polynomials [77.34726150561087]
  We show how to perform controllable reconstructions of a finite energy resolution with rigorous error estimates. This paves the way for future applications in nuclear and condensed matter physics.
  arXiv  Detail & Related papers  (2021-10-05T15:16:13Z)
• Visualizing spinon Fermi surfaces with time-dependent spectroscopy [62.997667081978825]
  We propose applying time-dependent photo-emission spectroscopy, an established tool in solid state systems, in cold atom quantum simulators. We show in exact diagonalization simulations of the one-dimensional $t-J$ model that the spinons start to populate previously unoccupied states in an effective band structure. The dependence of the spectral function on the time after the pump pulse reveals collective interactions among spinons.
  arXiv  Detail & Related papers  (2021-05-27T18:00:02Z)
• 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)
• Theoretical methods for ultrastrong light-matter interactions [91.3755431537592]
  This article reviews theoretical methods developed to understand cavity quantum electrodynamics in the ultrastrong-coupling regime. The article gives a broad overview of the recent progress, ranging from analytical estimate of ground-state properties to proper computation of master equations. Most of the article is devoted to effective models, relevant for the various experimental platforms in which the ultrastrong coupling has been reached.
  arXiv  Detail & Related papers  (2020-01-23T18:09:10Z)

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.