Hamiltonian (quantum mechanics)
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In quantum mechanics, the Hamiltonian is the operator associated with a system's total energy. It normally includes kinetic and potential energy and may also contain terms representing interactions, external fields, spin, or other physical effects.
The possible results of measuring the system's energy are the eigenvalues of the Hamiltonian. The corresponding eigenstates describe states with definite energy, and their collection forms the energy spectrum of the system.
The Hamiltonian governs time evolution through the Schrödinger equation. For a time-independent Hamiltonian, energy eigenstates evolve by acquiring phase factors, while a general quantum state can be expressed as a superposition of these eigenstates.
Its mathematical form depends on the system being modelled, such as a free particle, harmonic oscillator, atom, molecule, solid, or many-particle system. The operator is named after William Rowan Hamilton, whose reformulation of classical mechanics strongly influenced quantum theory.
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- URL: https://en.wikipedia.org/wiki/Hamiltonian_(quantum_mechanics)