that in the laboratory reference frame $ b^{\mu} = \{ b, {\bf 0} \} $, $ b = {\mathop{\rm const}\nolimits}$; let there also exist a constant homogeneous external magnetic field oriented along the $ z $-axis: $ {\bf H} = H {\bf e}_{z} $, $ H > 0 $.

One can, considering an electron with a definite energy so that $ \psi(t,{\bf r}) = e^{-iEt} \,
\Psi({\bf r}) $, represent the equations of motion for the field $ \psi $ resulting from (\[model\_L\]) in the hamiltonian form: $$\label{sol_HPsi_EPsi}
    H_{\rm D} \Psi = E \Psi,$$ where $ H_{\rm D} $ is the hermitian energy operator: $$\label{model_H}
    H_{\rm D} =
        {\boldsymbol}\alpha {\bf P} + \gamma^{0} m - e A^{0}
        + \mu H \gamma^{0} \Sigma_{3} - b \gamma^{5},$$ $ {\bf P} = {\bf p} + e {\bf A} $ is the canonical quantum-mechanical momentum, $ {\bf p} = -i \nabla $; $ {\boldsymbol}\alpha = \gamma^{0} {\boldsymbol}\gamma $, $ \Sigma_{i} = \frac{1}{2} \epsilon_{ijk} \sigma^{jk} $. In order to perform the quantization of the theory, one must solve the eigenvalue problem (\[sol\_HPsi\_EPsi\]) and find a complete system of the electron wave functions $ \{ \Psi \} $.

Solution of the equations of motion {#sol}
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