Effect of minimal lengths on electron magnetism. (English) Zbl 1113.81041

Summary: We study the magnetic properties of an electron in a constant magnetic field and confined by a isotropic two-dimensional harmonic oscillator on a space where the coordinates and momenta operators obey generalized commutation relations leading to the appearance of a minimal length. Using the momentum space representation we determine exactly the energy eigenvalues and eigenfunctions. We prove that the usual degeneracy of Landau levels is removed by the presence of the minimal length in the limits of weak and strong magnetic field.The thermodynamical properties of the system, at high temperature, are also investigated showing a new magnetic behaviour in terms of the minimal length.


81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
81V70 Many-body theory; quantum Hall effect
81R60 Noncommutative geometry in quantum theory
82D20 Statistical mechanics of solids
82D40 Statistical mechanics of magnetic materials
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