magnetic flux between successive (negative) $\ell$ states in the LLL.

There are troublesome issues here. The infinite degeneracy is difficult, but even more so is the dependency of the wave function on gauge choice. There are some gauge invariant properties in such a system, for example, the spectrum of energies. The wave function, on the other hand, is [*not*]{} gauge invariant, and for a change in gauge, $\vec{\bf A}
\rightarrow \vec{\bf A^\prime}$, there is a corresponding expected change in wave function,[@griffiths18] $$\vec{\bf A^\prime} \equiv \vec{\bf A} + \vec{\bf \nabla}\Lambda  \Longrightarrow \Psi^\prime \equiv e^{iq \Lambda/\hbar} \Psi,
\label{psi_transform}$$ where $\Lambda$ is an arbitrary real function of position and time, and $q$ is the charge of the particle. So the probability density, $|\Psi|^2$ is expected to be gauge invariant. And yet, even within the symmetric gauge, Eq. (\[gauge\_as\]), different choices of $(x_0,y_0)$ seemingly result in wave functions that differ by far more than a phase (and therefore probability densities that [*do differ*]{} from one another). The reason for this problem is that a degeneracy exists in the solution. An explicit calculation of the wave function transformation corresponding to that in Eq. (\[psi\_transform\]) between the Landau gauge (to be reviewed below) and the Symmetric 