hamiltonian (\[sol\_tilde\_H\]) formally describes an electron with an anomalous magnetic moment in an external magnetic field without Lorentz symmetry breaking. The corresponding problem (\[sol\_tilde\_Hphi\_Ephi\]) has been studied and solved in [@Ternov_Bagrov_Zhukovsky] (this work, however, deals with the physical electron with mass greater than zero; nevertheless it can be easily seen that in the case $ \tilde{m} < 0 $ one can, with the help of one more unitary transformation, $ \tilde{H}'_{\rm D} = \gamma^{5} \tilde{H}_{\rm D} \gamma^{5} $, effectively perform the change in the hamiltonian: $ \tilde{m} \rightarrow -\tilde{m} $, $ \tilde{\mu} \rightarrow -\tilde{\mu} $; after that all results obtained in [@Ternov_Bagrov_Zhukovsky] can be applied to $ \tilde{H}'_{\rm D} $).

Let us give here only the final results of the solution of the problem (\[sol\_Hphi\_Ephi\]). The energy values under investigation can be written as follows: $$\label{sol_E}
    E = \epsilon \sqrt{
        \left( \Pi + \tilde{\mu} H \right)^{2} + \tilde{p}^{2}
    }, \qquad
    \epsilon = \pm 1,$$ where $$\label{sol_Pi_values}
    \Pi =
        \zeta \sqrt{ \tilde{m}^{2} + 2eHn }, \quad
    n = 0, 1, \ldots, \quad
    \zeta = \begin{cases}
        \pm 1, & n > 0, \\
        -{\mathop{\rm sign}\nolimits}\tilde{m}, & n = 0. \\
    \end{cases}$$ The quantity $ \Pi $ is the eigenvalue of the electron 