  Suppose a classical electron is confined to move in the $xy$ plane under the
influence of a constant magnetic field in the positive $z$ direction. It then
traverses a circular orbit with a fixed positive angular momentum $L_z$ with
respect to the center of its orbit. It is an underappreciated fact that the
quantum wave functions of electrons in the ground state (the so-called lowest
Landau level) have an azimuthal dependence $\propto \exp(-im\phi) $ with $m\geq
0$, seemingly in contradiction with the classical electron having positive
angular momentum. We show here that the gauge-independent meaning of that
quantum number $m$ is not angular momentum, but that it quantizes the distance
of the center of the electron's orbit from the origin, and that the physical
angular momentum of the electron is positive and independent of $m$ in the
lowest Landau levels. We note that some textbooks and some of the original
literature on the fractional quantum Hall effect do find wave functions that
have the seemingly correct azimuthal form $\propto\exp(+im\phi)$ but only on
account of changing a sign (e.g., by confusing different conventions) somewhere
on the way to that result.
