The Impact of deformed space-phase parameters into HAs and HLM systems with the improved Hulthen plus Hellmann potentials model in the presence of temperature-dependent confined Coulomb potential within the framework of DSE

Abstract

In this work, the improved Hulthen plus Hellmann potentials model in the presence of temperature-dependent confined Coulomb potential ´ IHHPTd model is adopted as the quark-antiquark interaction potential for studying the mass spectra of heavy mesons in the three-dimensional nonrelativistic quantum mechanics noncommutative phase space (3DNRQm-NCSP) symmetries. In addition, we found another application for this potential through its description for hydrogen atoms He+, Li+2 and Be+. We solved the deformed Schrödinger equation analytically using the generalized Bopp’s shift method and standard perturbation theory. The new energy eigenvalues E (u,d)hy nc−n and (E hlm n−g, E hlm n−mand E hlm n−l ) for hydrogen atoms and heavy mesons such as charmonium cc and bottomonium cb and corresponding deformed Hamiltonian operators H nc hhp(r, Θ, θ, λ, λ, σ, σ, ²) and H nc hhp(r, Θ, θ, λ, λ, σ, σ, gs) were obtained, respectively. The present results are applied for calculating the new mass of heavy mesons. Four special cases were considered when some of the improved potential parameters were set to zero, resulting into improved Hellmann potential, improved Yukawa potential, improved Coulomb potential, and improved Hulthen potential, in ´ (3DNRQm-NCSP) symmetries. The limiting cases are analyzed for Θ, σ and χ −→ 0 are compared with those of literature.

The Influence of Deformation Phase-Space on Spectra of Heavy Quarkonia in Improved Energy Potential at Finite Temperature Model of Shrodinger Equation Via the Generalized Boob’s Shift Method and Standard Perturbation Theory

“…One of the most important applications in the extended model of pNRQCD is to calculate the modified mass spectra of the heavy quarkonium systems (the mass of the quarkonium bound state), such as charmonium and bottomonium mesons, which have the quark and antiquark flavor in the symmetries of NCQM under improved internal energy potential at finite temperature. To achieve this goal, we generalize the traditional formula [84][85][86][87][88][89][90][91], 𝑀 = 2𝑚 + 𝐸 which defines the total mass of the different quarkonium states (resonance masses), to the new form:…”

The Influence of Deformation Space-Space on High and Low Energy Spectra of Fermionic Particles and Spectra of Heavy Quarkonia with Improved Hulthén Plus Hyperbolic Exponential Inversely Quadratic Potential

“…The LHS of Eq. ( 78) 𝑀 hiq𝑝 𝑛𝑙 describes the spinaveraged mass spectra of HLM such as 𝑐𝑐, 𝑏𝑏, 𝑏𝑐, 𝑏𝑠, 𝑐𝑠, and 𝑏𝑞, 𝑞 = (𝑢, 𝑑) under the HHEIQP model in usual NR QM symmetries, [93][94][95][96], while the RHS is our generalization to this equation in ENRQM symmetries, 𝑚 𝑄 and 𝑚 𝑞 are the quark mass and the anti-quark mass, 𝐸 𝑛𝑟 𝑛𝑙 is the nonrelativistic energy under HHEIQP model which is determined in Eq. ( 73 (…”

Anisotropic Behavior of S-Wave and P-Wave States of Heavy Quarkonia at Finite Magnetic Field

“…The SE played a vital role to obtain not only the energy spectrum of the diatomic and polyatomic molecule but also the spectrum of the heavy quarkonium system. The solution of the SE for the different potentials, as found in [60][61][62][63], has been obtained using generalized Boopp's shift method and standard perturbation theory. In the present work, medium-modified potential [64] has been used to investigate the properties of the heavy quarkonia.…”