Stone’s theorem and its applications to particle properties.
Loading...
Date
October 27, 2019
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Most of the physical laws associated with quantum mechanics are formulated in a math ematical framework where observables are represented as self-adjoint operators in Hilbert
space. These self-adjoint operators are unbounded and therefore very hard to work with.
Stone’s theorem makes it a little bit easier by establishing a bijection between a strongly
continuous one-parameter group and self-adjoint operators.
We began with the needed terminology, and then proved the stones theorem. In addition,
we have indicated some applications of Stone’s theorem , particularly those associated with
quantum mechanics (dilation and rotation in the Cartesian coordinates)
Description
A thesis submitted to the Department of Mathematics in partial fulfillment of the requirements for the degree of Master of Philosophy (Pure Mathematics)
Keywords
Stone theorem, Applications, Particle properties