mgr Anna Pachoł

Presentation of Master Thesis "A quantum particle on a bounded region".

The aim of my Master Thesis was to introduce the observables and quantum dynamics on a bounded region. It was shown in this thesis, that different boundary conditions lead to different operators and hence to different physics. In the case, when there exist many self-adjoint extension of the operator, one has to choose which observable of the quantum system is the correct one. I considered also different potentials, for which energy operator is self-adjoint, so it can be a generator of the dynamics. On the end I introduced dynamics of the bounded quantum systems and explained how the particle is localized inside bounded region. I showed, that to obtain the correct description of trapped particle we can not ignore the exterior of the trap. I obtained interesting results in relation between localization of quantum particle inside bounded region and probability current through the barriers.