Hamiltonian

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In physics, Hamiltonian has two distinct but closely related meanings.

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

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.

In control theory, see Hamiltonian (control theory).

The various senses of "Hamiltonian" in math and physics are named after Irish mathematician, physicist Sir William Rowan Hamilton. (1805 – 1865)

Hamiltonian also refers to those who are supporters of views expressed by the eighteenth century American politician Alexander Hamilton, (1755 or 1757 – 1804).

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