The Quantum Mechanical Current of the Pauli Equation

Details The Quantum Mechanical Current of the Pauli Equation The Quantum Mechanical Current of the Pauli Equation

1998-07-14

arxiv.org/abs/physics/9807019v1

Am. J. Phys. 67 (1999) 916

Physics

Physics Education

8 pages, LATeX

Scientific paper

10.1119/1.19149

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.

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