In quantum mechanics, a stationary state is an eigenstate of a Hamiltonian, or in other words, a state of definite energy. Quantum mechanics is the study of mechanical systems whose dimensions are close to the Atomic scale such as Molecules Atoms Electrons In Mathematics, given a Linear transformation, an of that linear transformation is a nonzero vector which when that transformation is applied to it changes In Quantum mechanics, the Hamiltonian H is the Observable corresponding to the Total energy of the system 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. In Quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system 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. Quantum mechanics is the study of mechanical systems whose dimensions are close to the Atomic scale such as Molecules Atoms Electrons In Physics and other Sciences energy (from the Greek grc ἐνέργεια - Energeia, "activity operation" from grc ἐνεργός An excited state is any state with energy greater than the ground state. Excitation is an elevation in energy level above an arbitrary baseline energy state The ground state of a quantum field theory is usually called the vacuum state or the vacuum. In quantum field theory (QFT the forces between particles are mediated by other particles In Quantum field theory, the vacuum state (also called the vacuum) is the Quantum state with the lowest possible Energy. This vacuum means "absence of matter" or "an empty area or space" for the cleaning appliance see Vacuum cleaner.

If more than one ground state exists, they are said to be degenerate. Many systems have degenerate ground states, for example, the hydrogen atom. A hydrogen atom is an atom of the chemical element Hydrogen. The electrically neutral It turns out that degeneracy occurs whenever a nontrivial unitary operator commutes with the Hamiltonian of the system. In Functional analysis, a branch of Mathematics, a unitary operator is a Bounded linear operator U    H  →  In Mathematics, the commutator gives an indication of the extent to which a certain Binary operation fails to be Commutative. In Quantum mechanics, the Hamiltonian H is the Observable corresponding to the Total energy 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. The third law of Thermodynamics is a statistical law of nature regarding Entropy and the impossibility of reaching Absolute zero of Temperature Absolute zero is the point at which molecules do not move (relative to the rest of the body more than they are required to by a quantum mechanical effect called Zero-point Temperature is a physical property of a system that underlies the common notions of hot and cold something that is hotter generally has the greater temperature In Thermodynamics (a branch of Physics) entropy, symbolized by S, is a measure of the unavailability of a system ’s Energy 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 Materials science, a crystal is a Solid in which the constituent Atoms Molecules or Ions are packed in a regularly ordered repeating

See also

• Quantum number
• Quantum mechanic vacuum or vacuum state
• Virtual particle
• Excited state