The Brachistochrone Problem: From Euler to Quantum
Carlos Hermans (TU Delft - Applied Sciences)
Johan Dubbeldam – Mentor
Jos Thijssen – Mentor
Wolter Groenevelt – Graduation committee member
Miriam Blaauboer – Graduation committee member
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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.