Physics Problem

Since Sean Carroll at Cosmic Variance is doing a thing to explain everything you always wanted to know about quantum mechanics, but were afraid to ask, I thought of a question. It's not really appropriate for the forum Sean will be addressing, so I will mention it here.

In quantum mechanics, the state of a physical system is represented by a ray in Hilbert space, a generally infinite dimensional vector space. In classical mechanics, the state of a system is represented by a point in configuration space (or, in the case of the Hamiltonian description) by a point in a 2n dimensional symplectic manifold (where n is the number of degrees of freedom of the system). As Planck's constant h -> 0, the two descriptions should become equivalent.

How does one go from the Hilbert space description to the manifold in that case? Anybody know a good answer for this?

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