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Ground state

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).

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