Quantum information measures of conformal fractional non-relativistic systems in a Coulomb potential

Abstract In this work, we examine the quantum information characteristics of a hydrogen-like system under a Coulomb potential by using previously derived exact solutions of the generalized Schrödinger equation formulated within the conformable fractional framework. The approach introduces a fractional parameter $$(0 &lt; \alpha \le 1)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>0</mml:mn> <mml:mo>&lt;</mml:mo> <mml:mi>α</mml:mi> <mml:mo>≤</mml:mo> <mml:mn>1</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> , which permits a continuous transition between standard quantum mechanics and a fractional description. Utilizing these available analytical solutions, we determine the associated energy spectrum and wavefunctions and employ them to quantify the informational structure of the system. In particular, we calculate the Shannon entropy in both position and momentum spaces, along with the Fisher information, as fundamental indicators of uncertainty, spatial spreading, and sensitivity to local variations of the probability density. The results show that the fractional parameter $$(\alpha )$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>α</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> produces nontrivial corrections to these quantum information measures, indicating modifications in localization properties and momentum profiles. Also, the formalism recovers the conventional hydrogenic limit when $$(\alpha \rightarrow 1)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>α</mml:mi> <mml:mo>→</mml:mo> <mml:mn>1</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> , which validates the consistency of the formulation. In this context, these results show that the conformable fractional framework constitutes a consistent extension for analyzing quantum systems via information-theoretic quantities without modifying the exact solutions, providing a systematic approach to investigate deviations from integer-order dynamics.