Ground state

The ground state is the lowest-energy state available to a quantum system. It can still have nonzero energy because of quantum fluctuations or constraints on the system.

Hamiltonian (quantum mechanics): The operator representing a quantum system’s total energy and governing its time evolution. Its lowest eigenvalue and corresponding eigenstate define the system’s ground state.
Quantum state: A mathematical description that encodes the possible outcomes of measurements on a quantum system. A ground state is one particular quantum state, distinguished by its energy.
Quantum annealing: An optimization method that encodes solutions in a quantum system’s low-energy states and varies its Hamiltonian. Its goal is to steer the system toward a ground state encoding a low-cost solution.
Excited state: A quantum state with energy above the system’s ground-state energy. Excited states differ from the ground state by carrying additional energy.
Variational principle: A method that estimates a system’s ground-state energy using trial states and an energy bound. It provides a practical route to approximate ground states when exact solutions are unavailable.
Energy eigenstate: A state with a definite energy, represented by an eigenvector of the system’s Hamiltonian. For a time-independent Hamiltonian, the ground state is its lowest-energy eigenstate.
Density functional theory: A computational method for estimating electronic structure using electron density as its central variable. Many implementations seek the electronic ground-state density to predict material properties.
Thermal state: A statistical mixture of energy states describing a system in thermal equilibrium. At nonzero temperature, a system generally occupies a mixture rather than only its ground state.
Quantum fluctuation: A variation in a quantum observable arising from the uncertainty and dynamics of a quantum state. Fluctuations can persist in the ground state, leaving it with nonzero energy.
Energy spectrum: The set of allowed energy values of a physical system. The ground state occupies the lowest value in the system’s energy spectrum.

Linked from 22 pages