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The effective mass Klein–Gordon equation in one dimension for the Woods–Saxon potential is solved by using the Nikiforov–Uvarov method. Energy eigenvalues and the corresponding eigenfunctions are computed. Results are also given for the constant mass case.

This paper presents an open-source program called AIMpy built on Python language. AIMpy is a solver for Schrödinger-like differential equations using asymptotic iteration method (AIM). To confirm that the code works seamlessly, it has been shown through the paper, with recalculation of some previously studied eigenvalue examples, that the code can very well reproduce their results.

In this study, the Klein–Gordon equation (KGE) is solved with the attractive radial potential using the Nikiforov–Uvarov-functional-analysis (NUFA) method in higher dimensions. By employing the Greene–Aldrich approximation scheme, the approximate bound state energy equations as well as the corresponding radial wave function are obtained in closed form. Also, the expression for the scattering phase shift is obtained in D-dimensions. The effects of the screening parameter and the total angular momentum quantum number on the bound state energy and the scattering states’ phase shift are also studied numerically and graphically at different dimensions. An interesting result of this study is the inter-dimensional degeneracy symmetry for scattering phase shift. Hence, this concept is applicable in the areas of nuclear and particle physics.

Similar to how general relativity emerged, quantum mechanics resulted from experimental observations that made us radically rethink our previous assumptions. Scientists who study atoms need to solve these three equations. They are for a system with N electrons affected by the nucleus’s attractive Coulomb force and the repulsive force between each pair of electrons and other potentials. While general relativity has upended our large-scale conception of the universe, quantum mechanics calls into question all our intuition regarding particle physics. The Klein–Gordon (KG) resolution helps determine some physical systems and their properties by finding their bound states and eigenfunctions. These are resolved using analytical and numerical methods, as well as Coulomb and Yukawa potentials. In order to extract some of the first eigenvalues of the quantum mechanical system, we applied the Nikiforov–Uvarov (NU) method to the KG equation. The findings are significant for understanding nuclear charge radius, spin, nuclear diffusion and other topics in numerous theoretical physics and quantum chemistry fields because they are more generic and helpful.

We analyze the (discrete) spectrum of the semirelativistic "spinless-Salpeter" Hamiltonian

The relativistic quantum dynamics of the generalized Klein–Gordon (KG) oscillator having position-dependent mass in the Gödel-type space–time is investigated. We have presented the generalized KG oscillator in this space–time, and discussed the effect of Cornell potential and linear potential for our considered system. The modification from the parameters of position-dependent mass and characterizing the space–time for the energy spectrums are presented.

We apply the asymptotic iteration method to solve the radial Schrödinger equation for the Yukawa type potentials. The solution of the radial Schrödinger equation by using different approaches requires tedious and cumbersome calculations; however, we present that it is possible to obtain the bound state energy eigenvalues for any n and ℓ values easily within the framework of this method. We also show the perturbed application of this method for the same potential. Our results are in excellent agreement with the findings of the SUSY perturbation, 1/N expansion and numerical methods.

Atomic physicists have faced the challenge of solving the Schrödinger equation for a system composed of $N$ electrons that experience both the attractive Coulomb force from the nucleus and the repulsive Coulomb force between each pair of electrons. The resolution of the Schrödinger equation and finding the bound states and the eigenfunctions of the mentioned equation are resolved by using many different methods, both analytically and numerically, with generalized pseudo-harmonics and the Mie potential. The eigenvalues and corresponding eigenfunctions of the Schrödinger equation with pseudo-harmonics and the Mie potential are obtained with the Nikiforov–Uvarov method. The two potentials are a combination of at least two terms. In this work, the method of approximation that is used for solving secular equations is that of Nikiforov and Uvarov, which is mentioned above, and we applied it to the Schrödinger equation to obtain some of the first eigenvalues of the quantum mechanical system. After comparing the eigenvalues results with other earlier works, the method gave satisfactory solutions, as expected.