The Brachistochrone Problem: From Euler to Quantum

Bachelor thesis (2017)

Authors

C.A. Hermans Applied Sciences

Contributors

J.L.A. Dubbeldam (supervisor 1)
J.M. Thijssen (supervisor 1)
W.G.M. Groenevelt (supervisor 2)
M. Blaauboer (supervisor 2)
Faculty
Applied Sciences
Copyright: © 2017 Carlos Hermans
Euler Brachistochrone Maximum Fidelity Friction Brachistochrone Drag Brachistochrone Quantum Brachistochrone
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Published Date

11-07-2017

Language

English

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Faculty

Applied Sciences

Abstract

In this thesis I take a look at various aspects of the brachistochrone problem. In the first half I consider the classical brachistochrone problem, without friction, after which I generalize to also consider drag; friction proportional to the squared speed. I do this numerically, with the shooting method, and following some papers, which Euler wrote. Then I will look at how Euler's results compare to modern results and discuss how they are different. In the second half I consider the quantum brachistochrone problem, following a paper by A. Carlini, and afterwards I look at a related problem, where there is not enough time to change an electron spin between two predetermined states. This problem has been numerically solved in an example.

Files

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