- \sin{{\textstyle}\frac{\delta}{2}}, \qquad
    \beta  = \cos{{\textstyle}\frac{\delta}{2}} + \sin{{\textstyle}\frac{\delta}{2}}.$$ The expression (\[sol\_coeffs\]) is valid for all $ n $ and $ \tilde{m} $. It should be noted that expressions (\[sol\_E\]), (\[sol\_Pi\_values\]) for the energy $ E $ and the quantity $ \Pi $ and expression (\[sol\_coeffs\]) for the coefficients $ \{ c_{\mathfrak a} \} $ do not include the quantum number $ s $. This degeneracy is typical of the electron in a uniform magnetic field problem and is related to the invariance with respect to the choice of the position of the electron center of orbit.

Thus we have found the eigenvalues and obtained the orthonormalized eigenfunction system of the hamiltonian $ H_{\rm D} $; the full set of quantum numbers is $ \{ n, s, p, \zeta, \epsilon \} $, where $$n, s = 0, 1, \ldots, \quad
    -\infty < p < +\infty, \quad
    \zeta = \pm 1, \quad
    \epsilon = \pm 1.$$ The wave functions and the energy spectrum are formally similar in structure to those of the problem without Lorentz invariance breaking considered in [@Ternov_Bagrov_Zhukovsky]. However in our case, the parameters $ \tilde{m} $, $ \tilde{p} $, $ \tilde{\mu} $ are effective quantities depending, as well as 