The analysis of spin and spin-orbit coupling in quantum and classical physics by quaternions

It is shown that quaternions offer a simple elegant description of spin of a single particle, perhaps superior to that of conventional quantum mechanics. The spin operators are S_x=¹/₂i, S_y=¹/₂j and S_z=¹/₂k (in units where h(cross)=1). Quaternion angular functions Z_j^+or-, m_j are given, which are explicit expressions for mod l,s,j,m_j> in terms of the states mod l,s,m_l,m_s>. Use of these Z^+or- functions offer an elegant analysis of: (i) the relativistic hydrogen atom; (ii) problems in classical physics, such as the wave equation (in which 'spin' emerges as a feature of the mathematics). Consideration is given to a speculation that there is simultaneous 'reality' of all three components of spin. The quaternion quantum mechanical arguments developed here are not incompatible with the results of a recent experiment on phase change commutivity by Kaiser. George and Werner (1984).