Stone’s theorem and its applications to particle properties.

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October 27, 2019
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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)
A thesis submitted to the Department of Mathematics in partial fulfillment of the requirements for the degree of Master of Philosophy (Pure Mathematics)
Stone theorem, Applications, Particle properties