A theoretical physics preprint reports exact analytical expressions for the allowed energies and corresponding wave functions of a generalized Klein–Gordon oscillator in Som–Raychaudhuri space–time. The model includes a uniform magnetic field and compares a linear potential with a Cornell-type potential.
The main result is mathematical rather than experimental. The study uses analytical calculations only: it contains no empirical sample and no experimental or observational data. Its energy patterns and radial profiles therefore describe what the model produces under its chosen equations and inputs, not an effect measured in a physical system.
An equation-driven result
To obtain the spectrum, the authors apply the extended Nikiforov–Uvarov method. In the reported procedure, h(z) = h_n(z) serves as the quantization condition for energy eigenvalues, while the functions ϕ(z) and y_n(z) are combined to construct the eigenfunctions. In ordinary terms, the condition selects the energy values allowed by the model.
The paper presents this as a direct algebraic route. It gives explicit quantization conditions and closed-form wave-function solutions in terms of biconfluent Heun polynomials, without ansatz assumptions or series truncation. The reported solutions are therefore formulas within the model, rather than estimates drawn from a data set.
Across the comparisons, the Cornell-type potential generally yields larger energy eigenvalues than the linear potential when quantum numbers and parameter values are matched. That comparison applies to the two interaction choices studied under the stated geometry and uniform magnetic-field setting.
Different inputs, different levels
One table gives a concrete example for the linear-potential case. At n = 0 and l = 0, the listed positive energy eigenvalues are 4.53166 when α = 0.3, 4.7502 when α = 0.5, and 4.90384 when α = 0.8. In this example, the energy rises across the listed α settings.
The corresponding Cornell-type example is higher throughout. At n = 0 and l = 0, the listed values are 6.14859 at α = 0.3, 6.3820 at α = 0.5, and 6.5364 at α = 0.8. These figures illustrate the broader comparison reported by the authors while remaining tied to the selected model settings.
The tables also show a regular rise in energy with the radial quantum number n when the angular quantum number is fixed at l = 0. The pattern appears in both potential cases, according to the reported calculations.
The direction of the α pattern depends on the angular quantum number. For l = 0, the reported energy eigenvalues increase with α; for l ≠ 0, they decrease as α increases. The same parameter therefore does not shift every modeled state in the same direction.
The shape of the modeled states
The calculations also examine radial eigenfunctions, showing how the modeled states vary across the radial coordinate. In all plotted solutions, the radial wave functions vanish at large distances. The authors interpret that falloff as physically acceptable bound-state behavior within the model.
The profiles change with the state being examined and with the chosen interaction. Higher quantum states spread across a larger radial region and show more pronounced oscillations, while the degree of localization and the overall radial shape differ between the linear and Cornell-type potentials.
The plotted wave functions use arbitrary normalization. The figures can therefore be read for differences in shape, spread and oscillation, but they do not provide absolutely normalized radial probabilities.
A result with a narrow scope
The document is identified as arXiv:2608.20273v1 and dated 20 Aug 2026. It combines symbolic derivations, numerical evaluations of selected positive-energy levels and plots of radial functions, all within the stated theoretical model.
Because the study contains no empirical sample or observations, its numerical entries are model outputs rather than measurements of a physical system. The supplied analysis reports no statistical uncertainty or measurement error for the calculated spectra.
The scope is also limited to the two potential cases examined in the paper. The reported formulas do not by themselves demonstrate that the same method works across other potentials, geometries or relativistic wave equations; that broader applicability remains a suggestion for further testing.
Within its stated scope, the authors interpret the extended framework as a systematic algebraic alternative that produces exact spectra and closed-form eigenfunctions. The evidence supports the modeled parameter patterns and radial profiles reported here, rather than a general claim about all related physical systems.
The work was supported by the KLUBAP-350 Project. The authors declare no competing interests and state that all results needed to support the conclusions are provided in the manuscript.
Paper data and sources
Original title: Analytical Solutions of the Generalized Klein-Gordon Oscillator in Som-Raychaudhuri Space-Time via the Extended Nikiforov-Uvarov Method
Authors: Hale Karayer, Tolga Celik, Dogan Demirhan
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-20
DOI: Not available
Original paper · Full text