What is "bound state"

n. (context particle English) A composite of two or more particles that behaves as a single particle.

In quantum physics, a bound state describes a system where a particle is subject to a potential such that the particle has a tendency to remain localised in one or more regions of space. The potential may be either an external potential, or may be the result of the presence of another particle.

In quantum mechanics (where the number of particles is conserved), a bound state is a state in Hilbert space representing two or more particles whose interaction energy is less than the total energy of each separate particle, and therefore these particles cannot be separated unless energy is added from outside. The energy spectrum of the set of bound states is discrete, unlike the continuous spectrum of free particles.

(Actually, it is possible to have unstable "bound states", which aren't really bound states in the strict sense, with a net positive interaction energy, provided that there is an "energy barrier" that has to be tunnelled through in order to decay. This is true for some radioactive nuclei and for some electret materials able to carry electric charge for rather long periods.)

For a given potential, a bound state is represented by a stationary square-integrable wavefunction. The energy of such a wavefunction is negative.

In relativistic quantum field theory, a stable bound state of particles with masses shows up as a pole in the S-matrix with a center of mass energy which is less than . An unstable bound state (see resonance) shows up as a pole with a complex center of mass energy.