Bound state

A bound state or a bound state is in physics, a composite of two or more bodies or particles that behave as a single object. The definition may apply against the state in which a single particle ( elementary or complex ) from the other away ( free ), or even compared to the case that all parts of the whole are apart ( dispersed ).

In quantum mechanics is (if the number of particles is retained) of the bonded state is a state in the Hilbert space, which corresponds to two or more particles, the energy of interaction is negative. Therefore, the particles can not be separated, as long as no energy is expended. This to release the binding energy required is called binding energy. The energy levels of the bound state, in contrast to the continuous spectrum of the individual particles, discrete. There are also unstable bound states with positive interaction energy. This is possible when an "energy barrier " exists, which must be tunneled to the decay. This is the case for some of the radionuclides in its basic state and in general for many of excited states of atomic nuclei.

Generally can exist in a bound state, a stable potential when there is a standing wave function. The energies of these wave functions are negative.

In relativistic quantum field theories mn shows a bound state with n particles of masses m1, ..., as a pole in the S- matrix with a rest mass smaller than m1 ... mn. An unstable bound state (see resonance) arises dar. as a pole with complex focal mass

Examples

  • A proton and an electron can move independently of each other; as a complete system they then have positive energy. However, forming them under the influence of the Coulomb force a bound state, the hydrogen atom, the energy is negative. It is only the state with the smallest (ie, most negative ) energy of the ground state stable. All others, excited, states are unstable and decay to the ground state. In this case, photons are emitted.
  • An atomic nucleus has a bound state of the protons and neutrons.
  • A positronium atom is bonded, an unstable state of an electron and a positron. It is divided into (usually) two photons.
  • The proton is a bound state of three quarks (two up and one down); Quark has a respective quantenchromodynamische the color red, green or blue. Unlike the case of hydrogen, the individual quarks can never be separated (see confinement).

Mathematical Structure in quantum mechanics

Be a complex separable Hilbert space, is a one -parameter group of unitary operators on and a statistical operator on. Be an observable, and the induced probability distribution in terms of the Borel - algebra on. The development of induced by is bound with respect to known when, where.

Example: Let and the local observables. Be with a compact support and

  • If the state of development ", the wave packet is constantly moving to the right ", eg if for all, then in relation to the place no bound state.
  • If does not change with time, e.g. for all, then in relation to the location of a bound state.
  • Generally, if the time development of " moves only within a limited range ", then a linked state with respect to the site.
Free particle S-Matrix Instability Color confinement
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