Hamiltonian

It turns out that giving the position and momentum of a particle specifies a point
in a space called the ‘phase space’ or ‘state space’ of the particle. Mathematically this is often a
‘cotangent bundle’ — an important concept from the theory of manifolds. A cotangent bundle is
an example of a ‘symplectic manifold’, which in turn is an example of a more general thing called a
‘Poisson manifold’.



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