Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford / 2017 / S18 / 3 / 1 / Solution

In the source's Gaussian electromagnetic units, set $\mathbf{\Pi }=-i\hslash \nabla -e\mathbf{A}/c$ and take $\Phi =0$. ThenThe chosen gauge is independent of $x,z,t$, so simultaneous energy and canonical $p_x,p_z$ eigenstates justify the exponential ansatz. On the remaining spinors use ${\Pi }_x=p_x+eBy/c$, ${\Pi }_y=-i\hslash d/dy$, ${\Pi }_z=p_z$. The coupled equations are $(E-m{c}^2)\phi =c\sigma \cdot \Pi \chi$ and $(E+m{c}^2)\chi =c\sigma \cdot \Pi \phi$.