Quantum mechanics: A dynamical state whose state vector (or wave function) is an
→ eigenvector of an → operator
corresponding to a specified physical quantity.

In molecular quantum mechanics, any of → quantum states
corresponding to a particular → electron configuration
(i.e. an arrangement of the electron(s) in certain → orbitals).
The electron configuration with the lowest energy is called the
→ ground state. All
higher energy states are called → excited states.

In cosmology, a → dimensionless
parameter introduced by the → equation of state
representing the ratio of the pressure to the energy density of a fluid, such as the
→ dark energy: w = p/ρ.
The → deceleration or → acceleration
of an → expanding Universe
depends on this parameter (→ accelerating Universe).
A number of numerical values of this parameter are as follows:
for the → cosmological constant: w = -1, for
→ non-relativistic matter (present-day
→ baryons): w = 0, and
for → relativistic matter (photons, neutrinos):
w = +1/3. Together with
Ω(dark energy) and Ω(matter), w provides a three-parameter
description of the dark energy. The simplest parametrization of the dark energy
is w = constant, although w might depend on → redshift.

The condition of a particle or system of particles (especially an atom, nucleus, molecule)
after absorbing energy from outside and transiting to a higher
→ energy level than that of its
→ ground state. Excited states are transitory as they
lose energy through emissions or collisions and return to ground state.

A proposal regarding the initial state of the → Universe
prior to the → Planck era. This
→ no boundary hypothesis assumes an imaginary time in that epoch.
In other words, there was no real time before the → Big Bang,
and the Universe did not have a beginning. Moreover, this model treats the Universe like
a quantum particle, in an attempt to encompass → quantum mechanics
and → general relativity;
and attributes a → wave function to the Universe.
The wave function has a large value for our own Universe, but small, non-zero values
for an infinite number of other possible, parallel Universes.

Hartle, J., Hawking, S., 1983, "Wave function of the Universe," Physical Review D 28;
→ initial; → state.

Hoyle state

حالت ِ هویل

hâlat-e Hoyle

Fr.: état de Hoyle

An → excited state in the
→ triple alpha process leading to the production of
the most abundant → isotope of → carbon.
The existence of this state is of extreme astrophysical importance concerning the
→ nucleosynthesis of ^{12}C in stellar
→ cores: ^{4}He + ^{4}He ↔ ^{8}Be, ^{8}Be + ^{4}He ↔ ^{12}C^{*}, ^{12}C^{*}→ ^{12}C + γ.
The process proceeds as follows. First the unstable
→ ground state of ^{8}Be is formed in
the collision of two
→ alpha particles. Since ^{8}Be exists
roughly 7 x 10^{-17} sec, it must fuse with an alpha particle before breaking up.
However, the probability of three bodies merging simultaneously is extremely
low. Hoyle showed that the ^{12}C nucleus needs an excited state or
resonance at 7.68 MeV to provide for a high reaction probability.
The Hoyle state was soon found at 7.65 MeV with the predicted
→ spin and → parity.

In honor of the British astrophysicist Fred Hoyle (1915-2001), who predicted
this state in 1953 (Hoyle et al. 1953, Physical Review 92, 1095); it
was discovered by W. A. Fowler in 1957; → state.

Statistical physics: A state of a physical system that is described in
terms of the system's overall or average properties at a macroscopic
level (→ temperature,
→ pressure,
→ density,
→ internal energy, etc.).
A macrostate will generally consist of many different
→ microstates. In defining a macrostate we ignore what is
going on at the microscopic (atomic/molecular) level.
The → probability
of a certain macrostate is determined by how many
microstates correspond to this macrostate. Therefore, the greater the number of microstates
which lead to a particular macrostate, the greater the probability of observing that
macrostate. Same as → macroscopic state.
See also → entropy,
→ Boltzmann's entropy formula,
→ multiplicity.

An excited state in an atom, which is at the origin of
the spectral lines called → forbidden lines.
The time duration of the excited state being relatively long,
under laboratory conditions the atom cannot pass directly to the
ground state by emitting radiation. In the extremely rarefied interstellar medium,
however, such highly improbable transitions do occur.

Statistical physics: For a system made up of a large number of
components, a state of the system which is specified by describing the
current dynamical variables of each constituting component. For
example, for a gas system composed of a large number of molecules, the
microstate is defined by the set of quantities which defines the state
of each molecule in the system (position, velocity, vibration, etc.).
In practice, it is impossible to know perfectly the
microstate of a system. The aim of → statistical physics
is to relate
the macroscopic (average ) observables (→ pressure,
→ temperature, → internal energy)
to the microstate of the system. Also called → microscopic state.
See also → macrostate and → multiplicity.