In physics, a bound state is a composite of two or more building blocks (particles or bodies) that behaves as a single object. In quantum mechanics (where the number of particles is conserved), a bound state is a state in the Hilbert space that corresponds to two or more particles whose interaction energy is negative, and therefore these particles cannot be separated unless energy is spent. The energy spectrum of a bound state is discrete, unlike the continuous spectrum of isolated particles. (actually, it is possible to have unstable bound states with a positive interaction energy provided that there is a "energy barrier" that has to be tunnelled through in order to decay. This is true for some radioactive nuclei) Since antiquity, people have tried to understand the behavior of matter: why unsupported objects drop to the ground, why different materials have different properties, and so forth. ... A particle is Look up Particle in Wiktionary, the free dictionary In particle physics, a basic unit of matter or energy. ... A physical body is an object which can be described by the theories of classical mechanics, or quantum mechanics, and experimented upon by physical instruments. ... Jump to: navigation, search Fig. ... In mathematics, a Hilbert space is an inner product space that is complete with respect to the norm defined by the inner product. ... In physics, interaction energy is the contribution to the total energy that is caused by an interaction between the objects being considered. ... This article needs to be cleaned up to conform to a higher standard of quality. ... Quantum tunneling is the quantum-mechanical effect of transitioning through a classically-forbidden energy state. ...

In general, a stable bound state is said to exist in a given potential of some dimension if stationary wavefunctions exist (normalized in the range of the potential). The energy of these wavefunctions is negative. This article is about the building; for another meaning, see stability. ...

In relativistic quantum field theory, a stable bound state of n particles with masses m₁, ..., m_n shows up as a pole in the S-matrix with a center of mass energy which is less than m₁+...+m_n. An unstable bound state (see resonance) shows up as a pole with a complex center of mass energy. Albert Einsteins theory of relativity is a set of two theories in physics: special relativity and general relativity. ... Quantum field theory (QFT) is the application of quantum mechanics to fields. ... This article is about the building; for another meaning, see stability. ... The S-matrix is the matrix in quantum mechanics, scattering theory or quantum field theory that relates the final state in the infinite future ( out channels) and the initial state in the infinite past ( in channels). ... Instability in systems is generally characterized by some of the outputs or internal states growing without bounds. ... In physics, resonance is the tendency of a system to absorb more oscillatory energy when the frequency of the oscillations matches the systems natural frequency of vibration (its resonant frequency) than it does at other frequencies. ... Jump to: navigation, search In mathematics, the complex numbers are an extension of the real numbers by the inclusion of the imaginary unit i, satisfying . ...

Examples

• A proton and an electron can move separately; the total center-of-mass energy is positive, and such a pair of particles can be described as an ionized atom. Once the electron starts to "orbit" the proton, the energy becomes negative, and bound states - namely the hydrogen atom - is formed. Only the lowest energy bound state, the ground state is stable. The other excited states are unstable and will decay into bound states with less energy by emitting a photon.
• A positronium "atom" is an unstable bound state of an electron and a positron. It decays into photons.
• The proton itself is a bound state of three quarks (two up and one down; one red, one green and one blue). However, unlike the case of the hydrogen atom, the individual quarks can never be isolated. See confinement.
• A nucleus is a bound state of nucleons.

Properties In physics, the proton (Greek proton = first) is a subatomic particle with an electric charge of one positive fundamental unit (1. ... Jump to: navigation, search Properties The electron is a fundamental subatomic particle which carries a negative electric charge. ... A hydrogen atom is an atom of the element hydrogen. ... In physics, the ground state of a quantum mechanical system is its lowest-energy state. ... In quantum mechanics, an excited state of a system (such as an atom, molecule or nucleus) is any quantum state of the system that has a higher energy than the ground state (that is, more energy than the absolute minimum). ... For the Science Fiction weapon, as seen in Star Trek, see Photon torpedo. ... Positronium is a quasi-stable system consisting of a positron and its anti-particle, an electron, bound together into an exotic atom. ... In physics, resonance is the tendency of a system to absorb more oscillatory energy when the frequency of the oscillations matches the systems natural frequency of vibration (its resonant frequency) than it does at other frequencies. ... Jump to: navigation, search Properties The electron is a fundamental subatomic particle which carries a negative electric charge. ... The first detection of the positron in 1932 by Carl D. Anderson The positron is the antiparticle or the antimatter counterpart of the electron. ... For the Science Fiction weapon, as seen in Star Trek, see Photon torpedo. ... Properties In physics, the proton (Greek proton = first) is a subatomic particle with an electric charge of one positive fundamental unit (1. ... Jump to: navigation, search The Quake Army Knife (QuArK) is a multi-purpose tool for the games using engines similar to or based on the Quake engine by id software. ... For other uses of this term, see: Quark (disambiguation) 1974 discovery photograph of a possible charmed baryon, now identified as the Σc++ In particle physics, the quarks are subatomic particles thought to be elemental and indivisible. ... For other uses of this term, see: Quark (disambiguation) 1974 discovery photograph of a possible charmed baryon, now identified as the Σc++ In particle physics, the quarks are subatomic particles thought to be elemental and indivisible. ... The initialism QCD can mean: Quantum chromodynamics Quintessential Player, formerly known as Quintessential CD Quality, Cost, Delivery, A three-letter acronym used in lean manufacturing This page concerning a three-letter acronym or abbreviation is a disambiguation page — a navigational aid which lists other pages that might otherwise share the... The initialism QCD can mean: Quantum chromodynamics Quintessential Player, formerly known as Quintessential CD Quality, Cost, Delivery, A three-letter acronym used in lean manufacturing This page concerning a three-letter acronym or abbreviation is a disambiguation page — a navigational aid which lists other pages that might otherwise share the... The initialism QCD can mean: Quantum chromodynamics Quintessential Player, formerly known as Quintessential CD Quality, Cost, Delivery, A three-letter acronym used in lean manufacturing This page concerning a three-letter acronym or abbreviation is a disambiguation page — a navigational aid which lists other pages that might otherwise share the... This article is about a particle physics phenomenon. ... Jump to: navigation, search Nucleus can mean: The Nuclear Envelope The nucleus is enveloped by a pair of membranes enclosing a lumen that is continuous with that of the endoplasmic reticulum. ... In physics a nucleon is a collective name for the two baryons the neutron and the proton. ...

Bootstrap philosophy

According to the bootstrap philosophy, not only is a hydrogen atom a bound state of a proton and an electron, but a proton is a bound state of a hydrogen atom and an electron, and an electron is a bound state of a hydrogen atom and a proton.

See also

• Composite field
• Resonance