  The two-dimensionality of graphene and other layered materials can be
exploited to simplify the theoretical description of their plasmonic and
polaritonic modes. We present an analytical theory that allows us to simulate
these excitations in terms of plasmon wave functions (PWFs). Closed-form
expressions are offered for their associated extinction spectra, involving only
two real parameters for each plasmon mode and graphene morphology, which we
calculate and tabulate once and for all. Classical and quantum-mechanical
formulations of this PWF formalism are introduced, in excellent mutual
agreement for armchaired islands with $>10\,$nm characteristic size. Examples
of application are presented to predict both plasmon-induced transparency in
interacting nanoribbons and excellent sensing capabilities through the response
to the dielectric environment. We argue that the PWF formalism has general
applicability and allows us to analytically describe a wide range of 2D
polaritonic behavior, thus facilitating their use for the design of actual
devices.
