Applied Physics and Mathematics Annotation << Back The description of spin in the language of quaternion algebra M.A. Mikaelyan In non-relativistic quantum mechanics the particle with spin ½ is associated with the evolution of four real functions, which combine with each other in two complex functions that form a spinor. With the help of quaternion algebra an alternative variant of combining in one quaternion function was considered [1,2]. Ultimately a description of spin particle appears to be identical to the description of spinless particle; in all formulas instead of the usual imaginary unit the quaternion imaginary unit figures. At the same time, unlike standard description, «switching» of magnetic field by the use of well-known substitution in momentum operator leads to the correct value of intrinsic magnetic moment of the particle. Previously [1,3] the relativistic generalization of the description of spin particle has been formulated and corresponds to the usage of biquaternion algebra (biquaternion is a quaternion with complex components). As in non-relativistic case the wave function is a one-component quantity. It means an absence of matrices in the formalism; this fact considerably simplifies the consideration. In this article the more detailed consideration is presented. In particular, it is shown that the use of complex quaternion algebra allows (without the turning to Dirac equation) to obtain the wave equation, which is identical to Klein-Gordon equation. At the same time such an equation automatically takes into account the «direct» interaction between spin and the electromagnetic field. Significant attention in the article is given to the technical issues – in particular, to the obtaining the rules of the conversion from the quaternion to the traditional description. Keywords: quantum mechanics, spin, quaternion, biquaternion, Pauli equation, Dirac equation. Contacts: E-mail: mikhail@bk.ru Pp. 72-85.