Discussion on the Energy Parallax and the Relationship to Perturbation Theory in Mathematical Physics

Abstract

This work is a discussion on the energy parallax theory developed in [1] [2] based on the multiplicity of the solutions theorem. This theory is compared with the perturbation theory in mathematical physics. The perturbation theory uses the increment of a solution which can be formalized with a Taylor series development. With the energy parallax theory, the convergence property of the Taylor series of the energy of a system is the key to decide to include additional solutions, defined on the so-called energy spaces [2]. The development is supported using various examples in quantum mechanics (i.e. Rayleigh-Schr ö dinger perturbation theory) and wave theory with the Electromagnetic (EM) energy density (i.e. evanescent waves within the skin layer of a dielectric material). Finally, we discuss the Woodward effect [3] and the application of the energy parallax when assuming that the variations of EM energy density can trigger such effect within asymmetric cavities.