العربية
中国
Français
Deutsch
Ελληνική
हिन्दी
Italiano
日本語
Português
Русский
EspañolSTATIONARY STATE
(Redirected from Ground 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.
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).
In the approximation that the electrons do not interact, an atom, ion, or molecule is in its ground state when all of its electrons are in their lowest possible energy levels.
When an atom is in its ground state, its electrons fill the lowest energy orbitals completely before they begin to occupy higher energy orbitals, and they fill subshells usually in accordance with Hund's rule.
When we allow the electrons to interact, and treat them in a many-bodied way, then the ground state is simply the lowest energy state.
★ Quantum number
★ Quantum mechanic vacuum or vacuum state
★ Virtual particle
★ Excited 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.
| Contents |
| Ground state |
| See also |
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).
In the approximation that the electrons do not interact, an atom, ion, or molecule is in its ground state when all of its electrons are in their lowest possible energy levels.
When an atom is in its ground state, its electrons fill the lowest energy orbitals completely before they begin to occupy higher energy orbitals, and they fill subshells usually in accordance with Hund's rule.
When we allow the electrons to interact, and treat them in a many-bodied way, then the ground state is simply the lowest energy state.
See also
★ Quantum number
★ Quantum mechanic vacuum or vacuum state
★ Virtual particle
★ Excited state
This article provided by Wikipedia. To edit the contents of this article, click here for original source.
psst.. try this: add to faves
