2021/08/25 by Z. E. Musielak, Musielak, Z. E.
Engineering · Physics and Astronomy · #FOS: Physical sciences #General Physics (physics.gen-ph) #Geophysics and Sensor Technology #Quantum Mechanics and Non-Hermitian Physics
paper · pdf · doi:10.48550/arxiv.2109.03600
openalex publication_date 2021/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The irreducible representations of the extended Galilean group are used to derive infinite sets of symmetric and asymmetric second-order differential equations with constant coeffcients. All derived equations are local and their Lagrangians exist. It is shown that the asymmetric equations are Galilean invariant but the symmetric ones are not. By specifying quantum and classical physical settings, the constants in the equations are determined and the fundamental wave equations, including the Schrödinger, Schrödinger-like and new asymmetric equations, are obtained; the derived wave equation is non-fundamental. Formulation of wave theories based on the fundamental and non-fundamental wave equaions is considered, and physical implications of these theories on the wave description are discussed.