# Shannon Entropy of a Hydrogenic Impurity on a Conical Surface: Confinement and Aharonov–Bohm Effects

## TL;DR

This paper calculates the Shannon entropy of a hydrogenic impurity on a conical surface, considering the effects of magnetic flux and geometry.

## Contribution

The study derives analytical expressions for energy eigenvalues and wave functions, and evaluates Shannon entropy under Aharonov–Bohm flux and geometric confinement.

## Key findings

- Shannon entropy is computed in configuration and momentum spaces for low-lying states.
- Magnetic flux breaks degeneracy in entropies for states n, m and n, −m.
- The entropic sum satisfies the Bialynicki-Birula–Mycielski bound, confirming model consistency.

## Abstract

In this work, we solve the Schrödinger equation for a hydrogenic impurity located at the apex of a right circular cone, with the electron constrained to move on the conical surface of semi-aperture angle θ0 and subjected to an Aharonov–Bohm magnetic flux along the symmetry axis. Analytical expressions for the energy eigenvalues and normalized radial wave functions are obtained in terms of the principal quantum number n and the angular quantum number m, the magnetic flux ν, and the cone angle. The Shannon entropy is evaluated in both configuration and momentum spaces for several low-lying states, and its variation with ν and θ0 is analyzed in detail. When the magnetic flux vanishes, pairs of states n, m and n, −m share the same entropic behavior; for finite flux, this degeneracy is lifted and the entropies depend explicitly on the state, the cone geometry, and the flux strength. Finally, we verify that the entropic sum Sr+Sp fulfills the Bialynicki-Birula–Mycielski bound, providing an information-theoretic consistency check for the model.