Speaker: Moshe Shapiro (Depts. of Chemistry and Physics, University of British Columbia, Canada) Title: Derivation of the momentum-position uncertainty relation and the quantum evolution equations from Canonical Invariance, and a new Semiclassical relativistic approximation Time: Today, 15.15 Place: Fysisk Auditorium Abstract: Based on the fact that a physical point in phase space remains unchanged under (canonical) transformations between one pair of conjugate variables and another, we are able to prove the momentum- position uncertainty relation. We then use the same method to derive the relativistic “proper-time/ rest-energy” transformation matrices, from which we obtain the quantum evolution equation of the rest-energy with the proper-time. For inertial frames, these equations can be reduced to the usual time dependent Schroedinger (or Klein Gordon) equations, however they are also valid for ACCELERATING frames. A simple semiclassical approximation in which the general relativistic orbit equations are incorporated in our formula for the wave function for a free-particle in curved spaces is then provided and applied to the case of a particle near a gravitational singularity. Peter Staanum and Nicolai Nygaard