The Levy-Leblond equation in a magnetic field

The block form of the Dirac equation in a magnetic field is 

When formulating the Hamiltonian in atomic units, we prefer to have the choice between the original Hartree system (with 6 = 1/c) and an SI-based system or a system based on esu (with 6=1). The latter two lead formally to the same Hamiltonian, and for all three choices the potential of a point nucleus is —Z/r. 

We now make a change of the metric (15) in order to prepare the construction of the Levy-Leblond equation. 

The following well-known relations (together with the Coulomb gauge) have been used in the reformulation of (123)  

The Pauli equation is equivalent to the Levy-Leblond equation in a magnetic field, in the same sense as the Schrodinger equation is equivalent to the Levy-Leblond in the absence of a magnetic field. 

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