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The effect of singular potentials on the harmonic oscillator. (English) Zbl 1200.81063

Summary: We address the problem of a quantum particle moving under interactions presenting singularities. The self-adjoint extension approach is used to guarantee that the Hamiltonian is self-adjoint and to fix the choice of boundary conditions. We specifically look at the harmonic oscillator added of either a \(\delta \)-function potential or a Coulomb potential (which is singular at the origin). The results are applied to Landau levels in the presence of a topological defect, the Calogero model and to the quantum motion on the noncommutative plane.

MSC:

81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
81R60 Noncommutative geometry in quantum theory
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