In physics, the ground state of a quantum mechanical system is its lowest-energy state. An excited state is any state with energy greater than the ground state. The ground state of a quantum field theory is usually called the vacuum state or the vacuum. A black hole concept drawing by NASA. Physics (from the Greek, φυσικός (physikos), natural, and φύσις (physis), nature) is the science of the natural world dealing with the fundamental constituents of the universe, the forces they exert on one another, and the results produced by these forces. ... Fig. ... In physics, the term state is used in several related senses, each of which expresses something about the way a physical system is. ... In quantum mechanics, an excited state of a system (such as an atom, molecule or nucleus) is any quantum state of the system that has a higher energy than the ground state (that is, more energy than the absolute minimum). ... Quantum field theory (QFT) is the application of quantum mechanics to fields. ... In quantum field theory, the vacuum state, usually denoted , is the element of the Hilbert space with the lowest possible energy, and therefore containing no physical particles. ... For other uses, see vacuum cleaner and Vacuum (musical group). ...

If more than one ground state exists, they are said to be degenerate. Many systems have degenerate ground states, for example, the hydrogen atom. It turns out that degeneracy occurs whenever a nontrivial unitary operator commutes with the Hamiltonian of the system. A hydrogen atom is an atom of the element hydrogen. ... In functional analysis, a unitary operator is a bounded linear operator U on a Hilbert space satisfying U*U=UU*=I where I is the identity operator. ... For an electrical switch that periodically reverses the current see commutator (electric) In mathematics, the commutator gives an indication of how poorly a certain binary operation fails to be commutative. ... The Hamiltonian, denoted H, has two distinct but closely related meanings. ...

According to the third law of thermodynamics, a system at absolute zero temperature exists in its ground state; thus, its entropy is determined by the degeneracy of the ground state. Many systems, such as a perfect crystal lattice, have a unique ground state and therefore have zero entropy at absolute zero (because ln(1) = 0). The third law of thermodynamics was developed by Walther Nernst and is thus sometimes referred to as Nernsts theorem. ... In physics, absolute zero or sausage time is a fundamental lower bound on the temperature of a macroscopic system. ... Temperature is the physical property of a system which underlies the common notions of hot and cold; the material with the higher temperature is said to be hotter. ... For other uses of the term entropy, see Entropy (disambiguation) The thermodynamic entropy S, often simply called the entropy in the context of thermodynamics, is a measure of the amount of energy in a physical system that cannot be used to do work. ... Quartz crystal A crystal is a solid in which the constituent atoms, molecules, or ions are packed in a regularly ordered, repeating pattern extending in all three spatial dimensions. ...

See also

• quantum number
• quantum mechanic vacuum or vacuum state
• virtual particle