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The Symplectic Camel

Frieswijk, K. (2013) The Symplectic Camel. Bachelor's Thesis, Mathematics.

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Abstract

Recent advances in symplectic topology suggest that classical and quantum mechanics are much closer than might appear at first sight. After having discussed some general properties of Hamiltonian mechanics and symplectic topology, we will show that Heisenberg's uncertainty principle has left an footprint in classical mechanics. We do this by making use of a surprising theorem called Gromov's non-squeezing theorem (1985), which states that no canonical transformation can squeeze a ball B(r) with radius r through a circular hole with radius R in the phase plane, if R<r. This theorem was lovingly nicknamed "the symplectic camel".

Item Type: Thesis (Bachelor's Thesis)
Degree programme: Mathematics
Thesis type: Bachelor's Thesis
Language: English
Date Deposited: 15 Feb 2018 07:54
Last Modified: 15 Feb 2018 07:54
URI: http://fse.studenttheses.ub.rug.nl/id/eprint/11308

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