Due to the importance of gauge symmetry in all fields of physics, and motivated by an article
written almost three decades ago that warns against a naive handling of gauge transformations in the
Landau level problem (a quantum electron moving in a spatially uniform magnetic field), we point out
a proper use of the generators of dynamical symmetries combined with gauge transformation methods to
easily obtain exact analytical solutions for all Landau level-wavefunctions in arbitrary gauge. Our
method is different from the old argument and provides solutions in an easier manner and in a
broader set of geometries and gauges; in so doing, it eliminates the need for extra procedures (i.e.
a change of basis) pointed out as a necessary step in the old literature, and gives back the
standard simple result, provided that an appropriate use is made of the dynamical symmetries of the
system and their generators. In this way the present work will at least be useful for
university-level educa…