CONV SCHROEDINGER · Schroedinger operators: from measure convergence to spectral convergence
FP6 — Marie Curie Actions (Human Resources and Mobility)
- Duration
- 2004-12-01 → 2006-11-30
- EU contribution
- €150,079
- Participants
- 1
- Scheme
- EIF
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Results in brief
Final Activity Report Summary - CONV SCHROEDINGER (Schroedinger operators: from measure convergence to spectral convergence)
The project CONV SCHROEDINGER aimed to compare certain types of Schroedinger operators (equations). These operators were used to model a quantum particle interacting with a given environment and their range of application covered many fields, from chemistry to electronics. The main mathematical achievement was that, for a fairly general class of Schroedinger operators, we showed that they could be approximated by the so-called point-potential operators. Moreover, the energy spectra of the two operators should then be similar. This also made the mathematical result interesting from the practical point of view, because the energy spectrum yielded the physical properties of the given system. The task of computing the spectrum might turn out to be too difficult in many cases, while for point-potential operators it was easy and particularly suitable for computer calculations. Therefore, the approximation represented an alternative way to analyse the spectral, thus also the physical, properties of certain quantum-mechanical systems.
Data: CORDIS, © European Union
Project objective
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.
Original text from CORDIS.
Participants
- CHALMERS TEKNISKA HOEGSKOLA AB (CUT.MI) · GOTEBORGCoordinatorCity levelSweden
Links
Data: CORDIS, © European Union