Solution
= Solution
Separate $x,z$ <Plane wave>[plane waves] in the spinless equation. The transverse operator is $-\hbar^2d^2/dy^2+(p_x+eBy/c)^2$, the same shifted oscillator without a <Pauli term>. Its <Eigenvalue>[eigenvalues] are $|e|\hbar|B|(2n+1)/c$. Thus
$$
\boxed{E^2=m^2c^4+p_z^2c^2+|e|\hbar|B|c(2n+1),}
$$
which is the printed formula for $B>0$. The absence of the spin splitting is the substantive difference from the Dirac result.