The **ground state** of a quantum mechanical system is its lowest-energy state; the energy of the ground state is known as the zero-point energy of the system. 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. 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. It is also possible for the highest excited state to have absolute zero temperature for systems that exhibit negative temperature.

Read more about Ground State: Examples

### Other articles related to "ground state, state, ground":

**Ground State**- Examples

... The wave function of the

**ground state**of a particle in a one-dimensional well is a half-period sine wave which goes to zero at the two edges of the well ... the Planck constant, m is the mass of the particle, n is the energy

**state**(n = 1 corresponds to the

**ground**-state energy), and L is the width of the well ... The wave function of the

**ground state**of a hydrogen atom is a spherically-symmetric distribution centred on the nucleus, which is largest at the center and reduces exponentially at larger distances ...

... When a transition metal ion of configuration, to, is in octahedral surroundings, its

**ground state**may be low spin (LS) or high spin (HS), depending to a first approximation on the magnitude of the energy gap between ... More precisely, for, the

**ground state**arises from the configuration where the electrons occupy first the orbitals of lower energy, and if there are more than six electrons, the ... The

**ground state**is then LS ...

... a complex Hamiltonian is found whose

**ground state**describes the solution to the problem of interest ... with a simple Hamiltonian is prepared and initialized to the

**ground state**... By the adiabatic theorem, the system remains in the

**ground state**, so at the end the

**state**of the system describes the solution to the problem ...

... For example the

**ground state**of helium is known to fifteen digits ... we use the fact that this is in the

**ground state**... principle, in which two electrons cannot be in the same

**state**...

... For a ferromagnet > 0 and the

**ground state**of the Hamiltonian is that in which all spins are aligned parallel with the field ... The spin-lowering operator annihilates the

**state**with minimum projection of spin along the z-axis, while the spin-raising operator annihilates the

**ground state**with maximum ... Since for the maximally aligned

**state**, we find where N is the total number of Bravais lattice sites ...

### Famous quotes containing the words state and/or ground:

“No matter how corrupt and unjust a convict may be, he loves fairness more than anything else. If the people placed over him are unfair, from year to year he lapses into an embittered *state* characterized by an extreme lack of faith.”

—Anton Pavlovich Chekhov (1860–1904)

“Are not two sparrows sold for a penny? Yet not one of them will fall to the *ground* apart from your Father.”

—Bible: New Testament, Matthew 10:29.