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
