https://doi.org/10.1140/epjp/s13360-026-07320-5
Regular Article
Information entropy and thermodynamic properties with modified trigonometric inversely quadratic potential
1
Department of Mathematics, Federal University of Technology, Owerri, Imo State, Nigeria
2
Department of Physics, Chukwuemeka Odumegwu Ojukwu University, Uli, Anambra State, Nigeria
3
Department of Physics, Federal University of Technology, Owerri, Imo State, Nigeria
4
Electro-Optics and Photonics, University of Dayton, 45469, Dayton, OH, USA
5
Department of Science Laboratory Technology, Imo State Polytechnic, Omuma, Imo State, Nigeria
6
Department of Science Laboratory Technology, Federal Polytechnic, Oko, Anambra State, Nigeria
a
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Received:
30
December
2025
Accepted:
13
January
2026
Published online:
23
January
2026
Abstract
We analyze a quantum particle in the modified trigonometric inversely quadratic (MTIQ) potential—a pseudoharmonic well with a repulsive inverse-square core. Using the formula method, we derive bound-state energies and normalized wavefunctions; momentum-space states are obtained via a Fourier transform. We then evaluate Shannon information entropies in position and momentum space for representative states and analyze their dependence on quantum numbers and potential parameters. Increasing n (at fixed l) broadens both position and momentum densities, so information entropies in position and momentum space increase, and their sum satisfies the Białynicki–Birula–Mycielski (BBM) bound in all cases considered. Finally, we derive thermodynamic functions from the discrete spectrum using a Poisson-summation representation of the partition function and discuss the crossover from a gap-dominated low-temperature regime to an effectively harmonic high-temperature regime. We also summarize the stability condition associated with the inverse-square core.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2026
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
