Model potentials for quantum dots with smooth boundaries, realistic in the whole range of energies, are introduced, starting from the integrable motion of a particle on a sphere under the action of an external quadratic field. We show that in the case of rotational invariant potentials, the associated 2D Schrödinger equation has exact zero-energy eigenfunctions, in terms of which the whole discrete spectrum can be characterized.
Integrable systems on a sphere as models for quantum dots / Salerno, M.; De Filippo, S.; Tufino, E.; Enolskii, V. Z.. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND GENERAL. - ISSN 0305-4470. - 34:11(2001), pp. 2311-2317. [10.1088/0305-4470/34/11/322]
Integrable systems on a sphere as models for quantum dots
Tufino E.;
2001
Abstract
Model potentials for quantum dots with smooth boundaries, realistic in the whole range of energies, are introduced, starting from the integrable motion of a particle on a sphere under the action of an external quadratic field. We show that in the case of rotational invariant potentials, the associated 2D Schrödinger equation has exact zero-energy eigenfunctions, in terms of which the whole discrete spectrum can be characterized.
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