Bound state

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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 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.)

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 energies of these wavefunctions are negative.

In relativistic quantum field theory, a stable bound state of n particles with masses m1, ..., mn shows up as a pole in the S-matrix with a center of mass energy which is less than m1+...+mn. An unstable bound state (see resonance) shows up as a pole with a complex center of mass energy.


See also

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