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Encyclopedia > Canonical coordinates

In physics, the canonical commutation relation is the relation

among the position x and momentum p of a point particle in one dimension, where [x,p] = xp - px is the so-called commutator of x and p, i is the imaginary unit and is the reduced Planck's constant. This relation is attributed to Heisenberg, and it implies his uncertainty principle.

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Canonical coordinates - Wikipedia, the free encyclopedia (364 words)
In mathematics and physics, the canonical coordinates are a special set of coordinates on the cotangent bundle of a manifold.
A change of coordinates that preserves this form is a canonical transformation; these are a special case of a symplectomorphism, which are essentially a change of coordinates on a symplectic manifold.
When a Hamiltonian is defined on the cotangent bundle, then the generalized coordinates are related to the canonical coordinates by means of the Hamilton-Jacobi equations.
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