We argue that the process of constructing the quantum mechanical current of the Pauli equation by copying the line of arguments used in the spin-0 case, i.e. the Schr\"{ o}dinger equation, is ambiguous. We show that a non-relativistic reduction of the relativistic Dirac four-vector current is, however, capable of fully resolving the problem. This analysis reveals that the non-relativistic current of the Pauli equation should include an extra term of the form $\vec \nabla \vec \times (\psi^{ \dagger} \vec \sigma \psi)$. We present an initial exploration of the potential consequences of this new 'spin-term' by solving the Pauli equation for crossed magnetic and electric fields and calculating the corresponding current.
Categories: physics.ed-ph quant-ph