A novel algebraic approach for the Schrödinger equation in split quaternionic mechanics. (March 2023) - Guo, Zhenwei; Jiang, Tongsong; Vasil'ev, V.I.; Wang, Gang
Abstract: In the theoretical exploration and numerical computation of split quaternionic quantum mechanics, an important goal is to solve the Schrödinger equation ∂ ∂ t | f 〉 = − A | f 〉 with A an i -Hermitian split quaternion matrix, and | f 〉 an eigenstate to A . The split quaternionic Schrödinger equation is a fundamental equation in split quaternionic mechanics and plays an indispensable role. It is known that the problems of split quaternion Schrödinger equation can be discretized into the related eigen-problems of split quaternion matrix A α = α λ . This paper studies the problem of split quaternion Schrödinger equation based on an isomorphic mapping, derives a novel approach for Schrödinger equation in split quaternion mechanics. This paper also shows an algebraic approach to the eigen-problems for i -Hermitian split quaternion matrices. The algebraic approach will have potential applications in the research field of split quaternionic mechanics.