Bound states

In quantum physics, a bound state is a special quantum state of a particle 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 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. In general, the energy spectrum of the set of bound states is discrete, unlike 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." Examples include certain radionuclides and electrets.

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

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