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 Ssub(x) = (1/2)i, Ssub(y) = (1/2)j and Ssub(z) = (1/2)k (in units where (h/2π) = 1). Quaternion angular functions Z+-sub(j), msub(j) are given, which are explicit expressions for |l,s,j,msub(j)> in terms of the states |l,s,msub(l),msub(s)>. Use of these Z+-functions offers an elegant analysis of: (i) the relativistic hydrogen atom; (ii) problems in classical physics, such as the wave equation. Consideration is given to a speculation that there is simultaneous 'reality' of all three components of spin. (author)