quantum mechanics Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...

, an excited state of a system (such as an

atom Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons. Every solid, liquid, gas, and ...

molecule A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bioch ...

nucleus Nucleus ( : nuclei) is a Latin word for the seed inside a fruit. It most often refers to: *Atomic nucleus, the very dense central region of an atom * Cell nucleus, a central organelle of a eukaryotic cell, containing most of the cell's DNA Nucl ...

) is any

quantum state In quantum physics, a quantum state is a mathematical entity that provides a probability distribution for the outcomes of each possible measurement on a system. Knowledge of the quantum state together with the rules for the system's evolution in ...

of the system that has a higher

energy In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat a ...

than the

ground state The ground state of a quantum-mechanical system is its stationary state of lowest energy; 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. ...

(that is, more energy than the absolute minimum). Excitation refers to an increase in

energy level A quantum mechanical system or particle that is bound—that is, confined spatially—can only take on certain discrete values of energy, called energy levels. This contrasts with classical particles, which can have any amount of energy. The te ...

above a chosen starting point, usually the ground state, but sometimes an already excited state. The

temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer. Thermometers are calibrated in various temperature scales that historically have relied o ...

of a group of particles is indicative of the level of excitation (with the notable exception of systems that exhibit

negative temperature Certain systems can achieve negative thermodynamic temperature; that is, their temperature can be expressed as a negative quantity on the Kelvin or Rankine scales. This should be distinguished from temperatures expressed as negative numbers ...

). The lifetime of a system in an excited state is usually short: spontaneous or induced emission of a quantum of energy (such as a

photon A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they always ...

or a

phonon In physics, a phonon is a collective excitation in a periodic, Elasticity (physics), elastic arrangement of atoms or molecules in condensed matter physics, condensed matter, specifically in solids and some liquids. A type of quasiparticle, a phon ...

) usually occurs shortly after the system is promoted to the excited state, returning the system to a state with lower energy (a less excited state or the ground state). This return to a lower energy level is often loosely described as decay and is the inverse of excitation. Long-lived excited states are often called

metastable In chemistry and physics, metastability denotes an intermediate Energy level, energetic state within a dynamical system other than the system's ground state, state of least energy. A ball resting in a hollow on a slope is a simple example of me ...

. Long-lived

nuclear isomer A nuclear isomer is a metastable state of an atomic nucleus, in which one or more nucleons (protons or neutrons) occupy excited state, higher energy levels than in the ground state of the same nucleus. "Metastable" describes nuclei whose excited ...

s and

singlet oxygen Singlet oxygen, systematically named dioxygen(singlet) and dioxidene, is a gaseous inorganic chemical with the formula O=O (also written as or ), which is in a quantum state where all electrons are spin paired. It is kinetically unstable at ambie ...

are two examples of this.

Atomic excitation

Atoms can be excited by heat, electricity, or light. A simple example of this concept comes by considering the

hydrogen atom A hydrogen atom is an atom of the chemical element hydrogen. The electrically neutral atom contains a single positively charged proton and a single negatively charged electron bound to the nucleus by the Coulomb force. Atomic hydrogen consti ...

. The ground state of the hydrogen atom corresponds to having the atom's single

electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no kn ...

in the lowest possible orbital (that is, the spherically symmetric " 1s"

wave function A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system. The wave function is a complex-valued probability amplitude, and the probabilities for the possible results of measurements mad ...

, which, so far, has demonstrated to have the lowest possible quantum numbers). By giving the atom additional energy (for example, by the absorption of a

of an appropriate energy), the electron is able to move into an excited state (one with one or more quantum numbers greater than the minimum possible). If the photon has too much energy, the electron will cease to be

bound Bound or bounds may refer to: Mathematics * Bound variable * Upper and lower bounds, observed limits of mathematical functions Physics * Bound state, a particle that has a tendency to remain localized in one or more regions of space Geography *B ...

to the atom, and the atom will become

ionized Ionization, or Ionisation is the process by which an atom or a molecule acquires a negative or positive charge by gaining or losing electrons, often in conjunction with other chemical changes. The resulting electrically charged atom or molecule ...

. After excitation the atom may return to the ground state or a lower excited state, by emitting a photon with a characteristic energy. Emission of photons from atoms in various excited states leads to an

electromagnetic spectrum The electromagnetic spectrum is the range of frequencies (the spectrum) of electromagnetic radiation and their respective wavelengths and photon energies. The electromagnetic spectrum covers electromagnetic waves with frequencies ranging from ...

showing a series of characteristic

emission line A spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from emission or absorption of light in a narrow frequency range, compared with the nearby frequencies. Spectral lines are often used to iden ...

s (including, in the case of the hydrogen atom, the Lyman, Balmer, Paschen and Brackett series). An atom in a high excited state is termed a

Rydberg atom A Rydberg atom is an excited atom with one or more electrons that have a very high principal quantum number, ''n''. The higher the value of ''n'', the farther the electron is from the nucleus, on average. Rydberg atoms have a number of peculia ...

. A system of highly excited atoms can form a long-lived condensed excited state e.g. a condensed phase made completely of excited atoms:

Rydberg matter Rydberg matter is an exotic phase (matter), phase of matter formed by Rydberg atoms; it was predicted around 1980 by É. A. Manykin, M. I. Ozhovan and P. P. Poluéktov. It has been formed from various elements like caesium, potassium, hydrogen and ...

Perturbed gas excitation

A collection of molecules forming a gas can be considered in an excited state if one or more molecules are elevated to kinetic energy levels such that the resulting velocity distribution departs from the equilibrium

Boltzmann distribution In statistical mechanics and mathematics, a Boltzmann distribution (also called Gibbs distribution Translated by J.B. Sykes and M.J. Kearsley. See section 28) is a probability distribution or probability measure that gives the probability th ...

. This phenomenon has been studied in the case of a

two-dimensional gas A two-dimensional gas is a collection of objects constrained to move in a planar or other two-dimensional space in a gaseous state. The objects can be: classical ideal gas elements such as rigid disks undergoing elastic collision In physics, a ...

in some detail, analyzing the time taken to relax to equilibrium.

Calculation of excited states

Excited states are often calculated using

coupled cluster Coupled cluster (CC) is a numerical technique used for describing many-body systems. Its most common use is as one of several post-Hartree–Fock ab initio quantum chemistry methods in the field of computational chemistry, but it is also used in ...

Møller–Plesset perturbation theory Møller–Plesset perturbation theory (MP) is one of several quantum chemistry post–Hartree–Fock ab initio methods in the field of computational chemistry. It improves on the Hartree–Fock method by adding electron correlation effects by ...

multi-configurational self-consistent field Multi-configurational self-consistent field (MCSCF) is a method in quantum chemistry used to generate qualitatively correct reference states of molecules in cases where Hartree–Fock and density functional theory are not adequate (e.g., for mole ...

configuration interaction Configuration interaction (CI) is a post-Hartree–Fock linear variational method for solving the nonrelativistic Schrödinger equation within the Born–Oppenheimer approximation for a quantum chemical multi-electron system. Mathematical ...

, and

time-dependent density functional theory Time-dependent density-functional theory (TDDFT) is a quantum mechanical theory used in physics and chemistry to investigate the properties and dynamics of many-body systems in the presence of time-dependent potentials, such as electric or magne ...

Excited-state absorption

The excitation of a system (an atom or molecule) from one excited state to a higher-energy excited state with the absorption of a photon is called ''excited-state absorption'' (ESA). Excited-state absorption is possible only when an electron has been already excited from the ground state to a lower excited state. The excited-state absorption is usually an undesired effect, but it can be useful in upconversion pumping. Excited-state absorption measurements are done using pump–probe techniques such as

flash photolysis Flash photolysis is a pump-probe laboratory technique, in which a sample is first excited by a strong pulse of light from a pulsed laser of nanosecond, picosecond, or femtosecond pulse width or by another short-pulse light source such as a fla ...

. However, it is not easy to measure them compared to ground-state absorption, and in some cases complete bleaching of the ground state is required to measure excited-state absorption.

Reaction

A further consequence of excited-state formation may be reaction of the atom or molecule in its excited state, as in

photochemistry Photochemistry is the branch of chemistry concerned with the chemical effects of light. Generally, this term is used to describe a chemical reaction caused by absorption of ultraviolet (wavelength from 100 to 400 nm), visible light (400–7 ...

References

External links

NASA background information on ground and excited states
{{Authority control Quantum mechanics