Diatomic Molecules with the Improved Deformed Generalized Deng–Fan Potential Plus Deformed Eckart Potential Model through the Solutions of the Modified Klein–Gordon and Schrödinger Equations within NCQM Symmetries

Abstract

In this study, the deformed Klein–Gordon equation and Schr¨odinger equations were solved with the improved deformed generalized Deng–Fan potential plus the deformed Eckart potential (IDGDFDE-P, in short) model using Bopp’s shift and standard perturbation theory methods in the symmetries of extended quantum mechanics. By employing the improved approximation to the centrifugal term, the relativistic and nonrelativistic bound-state energies are obtained for some selected diatomic molecules such as N₂, I₂, HCl, CH, LiH, and CO. The relativistic energy shift ΔE^tot_dfe (n, a, c, b, V₀, V₁, V₂, Θ, σ, χ, j, l, s, m) and the perturbative nonrelativistic corrections ΔE^nr_dfe (n, α, c, b, V₀, V₁, V₂, Θ, σ, χ, j, l, s, m) appeared as functions of the parameters (α, c, b, V₀, V₁, V₂) and the parameters of noncommutativity (Θ, σ, χ), in addition to the atomic quantum numbers (n, j, l, s, m). In both relativistic and nonrelativistic problems, we show that the corrections to the energy spectrum are smaller than for the main energy in the ordinary cases of RQM and NRQM. A straightforward limit of our results to ordinary quantum mechanics shows that the present results under the IDGDFDE-P model is are consistent with what is obtained in the literature. In the new symmetries of noncommutative quantum mechanics (NCQM), it is not possible to get the exact analytical solutions for l = 0 and l  ̸ = 0. Only the approximate ones can be obtained. We have clearly shown that the Schr¨odinger and Klein–Gordon equations in the new symmetries can physically describe two Dirac equations and the Duffin–Kemmer equation within the IDGDFDE-P model in the extended symmetries.