Main Page | See live article | Alphabetical index In physics, the ground states of a system are its lowest-energy quantum mechanical states. If more than one lowest-energy 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. 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 crystal lattices, have a unique ground state and therefore have zero entropy at at absolute zero (because ln(1) = 0). See also: quantum number vacuum virtual particle This article is from Wikipedia. All text is available under the terms of the GNU Free Documentation License.