Quaternionic Wavefunction

Understand

We argue that quaternions form a natural language for the description of quantum-mechanical wavefunctions with spin.

• We use the quaternionic spinor formalism which is in one-to-one correspondence with the usual spinor language.
• No unphysical degrees of freedom are admitted, in contrast to the majority of literature on quaternions.
• In this paper we first build a Dirac Lagrangian in the quaternionic form, derive the Dirac equation and take the non-relativistic limit to find the Schr\"odinger's equation.