Shannon entropy of an electron on a conical surface: Aharonov–Bohm effects

Abstract In this work, we solve the Schrödinger equation of a particle restricted to move on a cone surface of finite height under the influence of an Aharonov–Bohm magnetic field. The energy eigenvalues and their respective wave functions are obtained analytically as a function of the radial distance from the apex and the apex angle. We compute the Shannon entropy in configuration and momentum space for the ground and the first excited states as a function of the slant height and the apex angle. In the absence of magnetic flux the states ( n,m ) and ( n ,− m ) have identical Shannon entropies, but for non-zero fluxes the Shannon entropies of these states are different, their values depending on the state, the apex angle and the value of the magnetic flux.