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, Mario;DE FILIPPO, Sergio;
2001-01-01
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.File in questo prodotto:
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