 Landau gauge for a uniform magnetic field

For $\mathbf{B}=B{\mathbf{e}}_z$, the vector potential $\mathbf{A}=(0,Bx,0)$ is a Landau gauge. Translation invariance in $y$ turns the transverse Hamiltonian into a family of harmonic oscillators in $x$ whose centres are labelled by the conserved $y$-momentum.