The quantum mechanical current of the Pauli equation

We argue that the process of constructing the quantum mechanical current of the Pauli equation by copying the line of argument used in the spin-0 case, i.e., the Schrödinger equation, is ambiguous. We show that a nonrelativistic reduction of the relativistic Dirac four-vector current is, however, capable of fully resolving the problem. This analysis reveals that the nonrelativistic current of the Pauli equation should include an extra term of the form ∇×(ψ†σψ). 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. © 1999 American Association of Physics Teachers.