# CONV SCHROEDINGER Sintesi della relazione

Project ID:
9256

Finanziato nell'ambito di:
FP6-MOBILITY

Paese:
Sweden

## 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.

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.