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Schroedinger operators: from measure convergence to spectral convergence

Ziel

The proposed project is aimed at the study of Schroedinger operators, which are differential operators of second order, used for modelling the behaviour of a quantum particle interacting with various types of potentials.

The objective is to approximate Schroedinger operators with one type of potentials by operators with another type of potentials, where the latter are solvable in the sense that their spectra are easy to calculate. It would yield an alternative method to compute the spectra in situations when a straightforward solution of partial differential equation is impracticable.

A special attention will be paid to singular potentials, namely the point potentials, as they represent a solvable model and they have been already successfully used for such approximation.

Due to the singular character of the potentials, first step is to explore the measure convergence of the operators, next step is to explain how it is reflected in the operator convergence and finally, one has to investigate the spectral convergence. Then the approximation will be eventually applied to particular, physically interesting systems.

Wissenschaftliches Gebiet (EuroSciVoc)

Thema/Themen

Aufforderung zur Vorschlagseinreichung

FP6-2002-MOBILITY-5
Andere Projekte für diesen Aufruf anzeigen

Finanzierungsplan

EIF - Marie Curie actions-Intra-European Fellowships

Koordinator

CHALMERS TEKNISKA HOEGSKOLA AB (CUT.MI)
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