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 / 3 / Solution

A simpler physical coordinate is $Y=y+p_{x}c/(eB)$. For ${\sigma }_3$ eigenvalue $s_z=\pm 1$, the equation becomes an oscillator of mass $m$, frequency ${\omega }_c=|eB|/(mc)$, and auxiliary energyIf the source's variable $\xi =(p_{x}c+eBy)/(\hslash c)=b_{B}Y$ is used literally, $b_B=eB/(\hslash c)$, then the same canonical oscillator form has $\boxed{M=m/b_B^2,\omega ={\omega }_c}$ and the same $\epsilon$. Because $\xi$ is an inverse length, this auxiliary $M$ is not a physical particle mass with ordinary mass dimensions; the rescaling must be carried through both kinetic and potential terms.