hamiltonian

In physics, Hamiltonian has distinct but closely related meanings.

In classical mechanics, the Hamiltonian is a function describing the state of a mechanical system in terms of position and momentum variables. See Hamiltonian mechanics.
In quantum mechanics, the Hamiltonian is an operator corresponding to the total energy of a system. See Hamiltonian (quantum mechanics).

In graph theory, a graph is Hamiltonian if it contains a path that starts and ends at the same vertex and includes each vertex exactly once. Such a path is called a Hamiltonian cycle. In group theory, see Hamiltonian group. Both the Hamiltonian operator in physics and Hamiltonian cycles in graph theory are named after Sir William Rowan Hamilton.

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