Algebraic techniques for Schrödinger equations in split quaternionic mechanics

Abstract

The split quaternionic Schrödinger equation ∂∂t|f〉=−A|f〉 plays an important role in split quaternionic mechanics, in which A a split quaternion matrix. This paper, by means of a real representation of split quaternion matrices, studies problems of split quaternionic Schrödinger equation, and gives an algebraic technique for the split quaternionic Schrödinger equation. This paper also derives an algebraic technique for finding eigenvalues and eigenvectors of a split quaternion matrix in split quaternionic mechanics.