The Brachistochrone Problem: From Euler to Quantum

Title

The Brachistochrone Problem: From Euler to Quantum

 Author

Hermans, Carlos (TU Delft Applied Sciences; TU Delft Electrical Engineering, Mathematics and Computer Science)

Contributor

Dubbeldam, Johan (mentor)
Thijssen, Jos (mentor)
Groenevelt, Wolter (graduation committee)
Blaauboer, Miriam (graduation committee)

Degree granting institution

Delft University of Technology

 Date

2017-07-11

 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.

 Subject

Euler
Brachistochrone
Maximum Fidelity
Friction Brachistochrone
Drag Brachistochrone
Quantum Brachistochrone

 To reference this document use:

http://resolver.tudelft.nl/uuid:3bc36b6d-eab1-4d20-afd2-1a1e0cc47a0f

 Part of collection

Student theses

 Document type

bachelor thesis

 Rights

© 2017 Carlos Hermans
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