Semi-classical theory for pedestrians

Tuesday 27 May, Wednesday 28 May, Tuesday 3 June, Wednesday 4 June and Tuesday 10 June

10-12am - Access Grid room, Welsh e-Science centre

 

Speaker: Professor U Smilanksy (Cardiff School of Mathematics, and Weizmann Institute of Sciences)

Starting from Feynman's path-integral formulation of quantum mechanics, I shall derive the semi classical expression for the evolution operator. As I go along, I shall explain a few basic concepts.
Switching gears to applications in spectral theory, I shall reduce the discussion to the pedestrian level, and derive a trace formula for systems in 1-d. As an application, I shall extract the Bohr-Sommerfeld quantization condition, and will close the cycle by using the Bohr-Sommerfeld condition to derive the trace formula once again. In this way I shall be able to introduce (with demonstrations) some of the main ideas and tools which are standard in the profession.