Talk:Symplectomorphism

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Help with this template Comments: edit – history – watch – refresh Arcfrk 01:44, 26 June 2007 (UTC)

[edit] QM

Heh. I just learned something today, which I think is utterly fascinating. Turns out the quantum-mechanical Schroedinger equation is nothing more (and nothing less!) than a purely classical Hamiltonian flow on CP^n. Heh! Here, a quantum mechanical state is regarded as a point in CP^n, i.e. a point on the Bloch sphere. Hamiltonian flows can be defined only if there is a symplectic form on the manifold... but of course, CP^n has the Fubini-Study metric, and so has the requisite symplectic form! Golly! This does have this forehead-slapping, "but of course, what else could it be" element to it, but .. well, I'm tickled. I'll have to work some sample problems in this new-found language. linas 04:25, 27 June 2006 (UTC)

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