Bound State

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 energy of these wavefunctions is negative.

In Relativistic Quantum Field Theory , a Stable bound state of n particles with masses m₁, ..., m_n shows up as a Pole in the S-matrix with a center of mass energy which is less than m₁+...+m_n. An Unstable bound state (see Resonance ) shows up as a pole with a Complex center of mass energy.

EXAMPLES

A Proton and an Electron can move separately; the total center-of-mass energy is positive, and such a pair of particles can be described as an ionized atom. Once the electron starts to "orbit" the proton, the energy becomes negative, and bound states - namely the Hydrogen Atom - is formed. Only the lowest energy bound state, the Ground State is stable. The other Excited State s are unstable and will decay into bound states with less energy by emitting a Photon .

A Nucleus is a bound state of Proton s and Neutron s ( Nucleon s).

A Positronium "atom" is an Unstable Bound State of an Electron and a Positron . It decays into Photon s.

The Proton itself is a bound state of three Quark s (two Up and one Down ; one Red , one Green and one Blue ). However, unlike the case of the hydrogen atom, the individual quarks can never be isolated. See Confinement .

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Bound State