  We point out a structural similarity between the characterization of black
hole apparent horizons as stable marginally outer trapped surfaces (MOTS) and
the quantum description of a non-relativistic charged particle moving in given
magnetic and electric fields on a closed surface. Specifically, the spectral
problem of the MOTS-stability operator corresponds to a stationary quantum
particle with a formal fine-structure constant $\alpha$ of negative sign. We
discuss how such analogy enriches both problems, illustrating this with the
insights into the MOTS-spectral problem gained from the analysis of the
spectrum of the quantum charged particle Hamiltonian.
