  In increasing the capabilities of the optical and microwave techniques
further into the subwavelength regime, quasistatic resonant structures has
attracted considerable interest. Electromagnetic responses of electrostatic
(ES) plasmon resonances in optics and magnetostatic (MS) magnon resonances in
microwaves give rise to a strong enhancement of local fields near the surfaces
of subwavelength particles. In the near-field regions of subwavelength
particles one can only measure the electric or the magnetic field with
accuracy. Such uncertainty in definition of the electric or magnetic field
components raises the question of energy eigenstates of quasistatic
oscillations. The energy eigenstate problem can be properly formulated when
potential functions, used in the quasistatic-resonance problems, are introduced
as scalar wave functions. In this case, one should observe quasistatic-wave
retardation effects still staying in frames of the quasistatic description of
oscillations in a subwavelength particle. In this paper, we analyze the problem
of energy quantization of ES resonances in subwavelength optical metallic
structures with plasmon oscillations and MS resonances in subwavelength
microwave ferrite particles with magnon oscillations. We show that in a case of
MS-potential scalar wave function one can observe quasistatic retardation
effects and obtain a proper formulation of the energy eigenstate problem.
