Two-Dimensional Electron Gas In A Non-Euclidean Space

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.