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Towards quantum and Brownian generalizations of classical geometric concepts

Apeldoorn, N. (2021) Towards quantum and Brownian generalizations of classical geometric concepts.

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Abstract:This work is a proof of concept of the idea that geometry can be reformulated based purely on quantum mechanical theory, rather than classical theory. The action plays a fundamental role in the fields of classical mechanics, quantum mechanics and brownian motion. We use the action to calculate probability distributions for the geometric concepts of area generalized in quantum mechanics and brownian motion. For this we use constrained path integrals to find the probability amplitude for a given area enclosed by a closed curve. We have found that the algebraic area enclosed by a curve in brownian motion is symmetrically distributed around zero and that this distribution converges to the classical result in the classical limit. The concept of Brownian area can be applied to quadrances in rational trigonometry to generalize trigonometric concepts and theorems.
Item Type:Essay (Bachelor)
Faculty:EEMCS: Electrical Engineering, Mathematics and Computer Science
Programme:Applied Mathematics BSc (56965)
Link to this item:http://purl.utwente.nl/essays/88756
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