Abstract:We consider a fractional generalization of two-dimensional (2D) quantum-mechanical Kepler problem corresponding to 2D hydrogen atom. Our main finding is that the solution for discreet spectrum exists only for µ > 1 (more specifically 1 < µ ≤ 2, where µ = 2 corresponds to "ordinary" 2D hydrogenic problem), where µ is the Lévy index. We show also that in fractional 2D hydrogen atom, the orbital momentum degeneracy is lifted so that its energy starts to depend not only on principal quantum number n but also on or… Show more
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