Abstract
Abstract
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
E
̄
(
2
)
. In this paper, we revisit the well-known energy eigenvalues of the system, known as the Landau levels, by exploiting the related
e
̄
(
2
)
symmetry algebra. Specifically, we utilize the Casimir operator and the commutation relations of the generators of the
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
E
̄
(
2
)
group and their implications on the degeneracy of Landau levels is discussed.
Subject
General Physics and Astronomy
Reference17 articles.
1. Über das wasserstoffspektrum vom standpunkt der neuen quantenmechanik;Pauli;Z. Phys.,1926
2. Zur theorie des wasserstoffatoms;Fock;Z. Phys.,1935
3. On the problem of degeneracy in quantum mechanics;Jauch;Phys. Rev.,1940
4. Diamagnetismus der metalle;Landau;Z. Phys.,1930
5. Magnetische widerstandsvergrösserung in einkristallen von wismut bei tiefen temperaturen;Schubnikow;Proc. R. Neth. Acad. Arts Sci.,1930
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