Analytical Solutions for a Supersymmetric Wave‐Equation for Quasiparticles in a Quantum System

Abstract Vortices and quasiparticles have been studied for 2D systems over the past decades in relation to the development of technologies in quantum electromagnetics, optics, and quantum computation. Deriving new equations for quasiparticles in quantum systems is therefore a critical part of quantum physics. Recently, a supersymmetric wave equation has been developed which describes quasiparticles and vorticity under the influence of electromagnetic fields which has been studied numerically. The analytical solutions of the supersymmetric wave‐equation are presented by increasing levels of energy. It is shown that the derived linear and nonlinear models of the supersymmetric wave‐equation can represent respectively symmetric and asymmetric vorticity formed in a confined rotating torus. The models described are suitable to represent vorticity formed in 2D and 3D electron gas and can be of significant relevance to future research in quantum electromagnetics.