# Stationary state

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Stationary state

In quantum mechanics, a stationary state is an eigenstate of a Hamiltonian, or in other words, a state of definite energy. It is called "stationary" because the corresponding probability density has no time dependence.

As an eigenstate of the Hamiltonian, a stationary state is not subject to change or decay (to a lower energy state). In practice, stationary states are never truly "stationary" for all time. Rather, they refer to the eigenstate of a Hamiltonian where small perturbative effects have been ignored. The language allows one to discuss the eigenstates of the unperturbed Hamiltonian, whereas the perturbation will eventually cause the stationary state to decay. The only true stationary state is the ground state.

Ground state

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.

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.

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).

ee also

*Quantum number
*Quantum mechanic vacuum or vacuum state
*Virtual particle

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• stationary state — stacionarioji būsena statusas T sritis Energetika apibrėžtis Sistemos būsena, kai termodinaminiai būsenos parametrai laikui bėgant nekinta. atitikmenys: angl. stationary state vok. stationärer Zustand, m rus. стационарное состояние, n pranc. état …   Aiškinamasis šiluminės ir branduolinės technikos terminų žodynas

• stationary state — /steɪʃənri ˈsteɪt/ (say stayshuhnree stayt) noun an energy state of a system, as an atom or molecule, when it is not emitting electromagnetic radiation …   Australian English dictionary

• stationary state — noun 1. : a stable or metastable quantum state 2. : a condition taken as an operational concept in economic analysis in which economic processes merely reproduce themselves with no changes …   Useful english dictionary

• stationary state — Physics. any of several energy states an atom may occupy without emitting electromagnetic radiation. * * * …   Universalium

• non-stationary state — nestacionarioji būsena statusas T sritis automatika atitikmenys: angl. non stationary state; nonstationary state; non steady state; unstable state vok. nichtstationärer Zustand, m rus. нестационарное состояние, n pranc. état non stationnaire, m …   Automatikos terminų žodynas

• non-stationary state — nenuostovioji būsena statusas T sritis Standartizacija ir metrologija apibrėžtis Būsena, kai sistemos parametrų vertės priklauso nuo laiko. atitikmenys: angl. non stationary state; non steady state vok. nichtstationärer Zustand, m rus.… …   Penkiakalbis aiškinamasis metrologijos terminų žodynas