Bound state

A bound state is a composite of two or more fundamental building blocks, such as particles, atoms, or bodies, that behaves as a single object and in which energy is required to split them.^[1]

In quantum physics, a bound state is a quantum state of a particle subject to a potential such that the particle has a tendency to remain localized in one or more regions of space.^[2] The potential may be external or it may be the result of the presence of another particle; in the latter case, one can equivalently define a bound state as a state representing two or more particles whose interaction energy exceeds the total energy of each separate particle. One consequence is that, given a potential vanishing at infinity, negative-energy states must be bound. The energy spectrum of the set of bound states are most commonly discrete, unlike scattering states of free particles, which have a continuous spectrum.

Although not bound states in the strict sense, metastable states with a net positive interaction energy, but long decay time, are often considered unstable bound states as well and are called "quasi-bound states".^[3] Examples include radionuclides and Rydberg atoms.^[4]

In relativistic quantum field theory, a stable bound state of n particles with masses ${\displaystyle \{m_{k}\}_{k=1}^{n}}$ corresponds to a pole in the S-matrix with a center-of-mass energy less than ${\displaystyle \textstyle \sum _{k}m_{k}}$. An unstable bound state shows up as a pole with a complex center-of-mass energy.