The seminar is sponsored by NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai.
Abstract:
The Schroedinger equation is of central importance in quantum physics. The eigenfunctions and eigenvalues of the Schroedinger operator represent bound states and their energies. In this talk we consider the bound states and energies for a particle in an external potential. In the first part of the talk, we discuss some old and new results concerning the energy of shallow bound states in two space dimensions. For central potentials the Jost function formalism can be used to calculate the energy of the weakly bound state, while for non-central potentials a different approach is required. In the second part of the talk, the relation between central and non-central potentials is considered. Specifically, we study the relationship between the bound-state energies of a non-central potential and those of its spherical average. It is shown that the two ground-state energies satisfy an inequality, and there is a similar inequality for the first excited states.
Biography:
Alexander Pikovski holds a M.S. from Cambridge University and got his PhD at the Leibniz University Hannover (Germany) in Theoretical Physics. He has been a postdoctoral researcher at the University of Hamburg and at the University of Colorado-Boulder. His research interests include cold gases, quantum many-body physics, and scattering theory.