Symbol H. A function used to express the energy of a system in terms of its momentum and positional coordinates. In simple cases this is the sum of its kinetic and potential energies. In Hamiltonian equations, the usual equations used in mechanics (based on forces) are replaced by equations expressed in terms of momenta. This method of formulating mechanics (Hamiltonian mechanics) was first introduced by Sir William Rowan Hamilton (1805–65). The Hamiltonian operator is used in quantum mechanics in the Schrödinger equation.