Abstract

MAIRECHE, A.. The impact of deformed space-phase parameters into HAs and HLM systems with the improved Hulthén plus Hellmann potentials model in the presence of temperature-dependent confined Coulomb potential within the framework of DSE. Rev. mex. fis. [online]. 2022, vol.68, n.5, e50702.  Epub Feb 17, 2023. ISSN 0035-001X.  https://doi.org/10.31349/revmexfis.68.050702.

In this work, the improved Hulthén 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 $E_{nc-n}^{\left(u,d\right)hy}$ and $E_{n-g}^{hlm}$, $\left(E_{n-m}^{hlm}\right.$ and $\left.E_{n-l}^{hlm}\right)$ for hydrogen atoms and heavy mesons such as charmonium c$\stackrel{-}{c}$ and bottomonium c$\stackrel{-}{b}$ and corresponding deformed Hamiltonian operators $H_{hhp}^{nc}$(r, Θ,$\stackrel{-}{\theta }$, λ,$\stackrel{-}{\lambda }$, σ,$\stackrel{-}{\sigma }$,𝜖) and $H_{hhp}^{nc}$(r, Θ,$\stackrel{-}{\theta }$, λ,$\stackrel{-}{\lambda }$, σ,$\stackrel{-}{\sigma }$, g s ) 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 Hulthén potential, in (3DNRQm-NCSP) symmetries. The limiting cases are analyzed for Θ, σ and χ → 0 are compared with those of literature.

Keywords : Schrödinger equation; Hulthen plus Hellmann potentials model; noncommutative quantum mechanics; star product; generalized Bopp’s shift method.

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