  The planar Landau system which describes the quantum mechanical motion of a
charged particle in a plane with a uniform magnetic field perpendicular to the
plane, is explored within pedagogical settings aimed at the beginning graduate
level. The system is known to possess the Euclidean symmetry in two dimensions
with central extension $\bar{E}(2)$. In this paper, we revisit the well-known
energy eigenvalues of the system, known as the Landau levels, by exploiting the
related $\bar{e}(2)$ symmetry algebra. Specifically, we utilize the Casimir
operator and the commutation relations of the generators of the $\bar{E}(2)$
group. More importantly, an algebraic formalism on this topic based on
Schwinger's oscillator model of angular momentum is also presented. The
dimensions of irreducible representations of the $\bar{E}(2)$ group and their
implications on the degeneracy of Landau levels is discussed.

Quantum Physics;High Energy Physics - Theory