In physics, a bound state is a composite of two or more building blocks (particles) that behaves as a single object.

In quantum mechanics, 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 bound states is discrete, unlike the continuous spectrum of isolated particles.

For example, 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 a stable bound state - namely the Hydrogen atom - is formed.

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.

A positronium is an unstable bound state because 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.

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 (quantum field theory)) shows up as a pole with a complex center of mass energy.

See also resonance (quantum field theory), composite field