The surface plasmon is the collective behavior of free electrons in the metal surface. Plasmon resonance is quantum mechanical or classical phenomena?
You can get a precise enough approximation of plasmon resonances through classical electromagnetics.
is reviewed in terms of both classical and quantum mechanical approaches. beside that all classical phenomena can be understood quantum mechanically
reference
Quantum mechanical origin of the plasmon: from molecular systems to nanoparticles 2014
As others alluded the plasmon resonance can always be understood quantum mechanically, and it can sometimes be understood classically. The canonical "classical" example is the bulk plasmon mode in an actual plasma of free electrons and, heavy, charged nuclei. In this case the plasmon resonance is the collective oscillation of the electrons with the effective restoring force arising from the neutralizing background of ions. For this system introducing quantum mechanics would only obfuscate the relevant physics provided temperature is far above the Fermi temperature.
On the other hand, an example that can only be understood quantum mechanically is the bulk plasmon mode in graphene. The linear dispersion of graphene is unlike other two-dimensional-electron-gases (e.g., GaAs systems, electrons floating on liquid He, which have a parabolic dispersion) and changes the scaling factor for the plasmon dispersion to explicitly depend on hbar instead of just the effective mass. This is true even in the high-temperature limit (where the role of Fermi degeneracy can be neglected).
Of course this boils down to a similar statement the previous commenter made: electronic structure in solids can only be understood with quantum mechanics. However, in the case of graphene this manifests itself explicitly in the plasmon dispersion of the conduction electrons, instead of just renormalizing the classical parameters as in other metallic systems.
In my point of view, the resonance could be explained explicitly by classical electro-dynamics. The resonance happens when the dielectric constant at some angular frequency of incident electromagnetic waves reaches singularity point (similar with the forced vibration) where the dielectric constant's relation of angular frequency could be calculated from classical model (the Lorenz model, for an example).
However, for a more in-depth understanding in plasmon resonance (rather than a phenomenological understanding which defines many undetermined parameters ), especially in the Surface Plasmon Polariton (SPP), the concept of polariton was introduced, which means a couple between photon and some material wave (plasmon, phonon, etc). In this point of view, the resonance (coupling) happens when the dispersion relations of plasmon and polariton intersect.
The European Physical Journal Plus
March 2016, 131:54
Improvement of the Exp-function method for solving the BBM equation with time-dependent coefficients
Maghsoud Jahani, Jalil Manafian
Regular Article
First Online:
08 March 2016
DOI: 10.1140/epjp/i2016-16054-2
Cite this article as:
Jahani, M. & Manafian, J. Eur. Phys. J. Plus (2016) 131: 54. doi:10.1140/epjp/i2016-16054-2
1 Citations 47 Views
Abstract.
In this article, we establish the exact solutions for the BBM equation with time-dependent coefficients. The Exp-function method (EFM) and improvement of the Exp-function method (IEFM) are used to construct solitary and soliton solutions of nonlinear evolution equations. These methods are developed for searching exact travelling wave solutions of nonlinear partial differential equations. The exact particular solutions are of four types: the hyperbolic function solution, trigonometric function solution, exponential solution and rational solution. It is shown that the EFM and IEFM, with the help of symbolic computation, provide a straightforward and powerful mathematical tool for solving nonlinear evolution equations in mathematical physics.
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