In 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 that corresponds to 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 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.
Read more about Bound State: Examples, In Mathematical Quantum Physics
Famous quotes containing the words bound and/or state:
“Edith: This complete loveliness will fade. And we shall forget what it was like.
Edward: Edith, don’t.
Edith: Oh, it’s bound to. Just a few years and the gilt wears off the gingerbread.
Edward: Darling, answer me one thing truthfully. Have you ever seen gingerbread with gilt on it?
Edith: [laughing] Fool!
Edward: Then the whole argument is disposed of.”
—Reginald Berkeley (1890 N1935)
“A State, in idea, is the opposite of a Church. A State regards classes, and not individuals; and it estimates classes, not by internal merit, but external accidents, as property, birth, etc. But a church does the reverse of this, and disregards all external accidents, and looks at men as individual persons, allowing no gradations of ranks, but such as greater or less wisdom, learning, and holiness ought to confer. A Church is, therefore, in idea, the only pure democracy.”
—Samuel Taylor Coleridge (1772–1834)