The analogue quantum mechanical of plasmonic atoms

Localized plasmons in metallic nanostructures present strong analogies with Quantum Mechanical problems of particles trapped in potential wells. In this paper we take this analogy further using the Madelung Formalism of Quantum Mechanics to express the fluid equations describing the charge density of the conduction electrons and corresponding interaction with light in terms of an effective generalized Non-linear Schr¨odinger equations. Within this context, it is possible to develop the analogy of a plasmonic atom and molecule that exhibits Rabi oscillations, Stark effect, among other Quantum Mechanical effects.