Abstract
A charged particle in the presence of a perpendicular magnetic field is
studied within the position-dependent translation operator formalism. We
show that the solution of the resulting Schro?dinger-like equation is
mapped on the Morse oscillator, instead of the expected quantum harmonic
oscillator. The anharmonicity that shows up naturally from the theory is
analogous to corrections introduced by relativistic effects. Due to the
nonEuclidean space, it is demonstrated that: (i) the degeneracy of the
spin up and spin down levels is lifted and (ii) the Fermi energy and the
total ground state energy of the two-dimensional electron gas is also
modified.
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