Editing Bound state (section)

{{Short description|Quantum physics terminology}}

A '''bound state''' is a composite of two or more fundamental building blocks, such as particles, atoms, or bodies, that behaves as a single object and in which energy is required to split them.<ref>{{Cite web|url=https://www.oxfordreference.com/display/10.1093/oi/authority.20110803095520865|title=Bound state - Oxford Reference}}</ref>

In [[quantum physics]], a bound state is a [[quantum state]] of a [[particle]] subject to a [[potential energy|potential]] such that the particle has a tendency to remain localized in one or more regions of space.<ref>{{cite book | last=Blanchard | first=Philippe | last2=Brüning | first2=Erwin | title=Mathematical Methods in Physics | publisher=Birkhäuser | date=2015 | isbn=978-3-319-14044-5|page=430}}</ref> 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 [[vanish at infinity|vanishing at infinity]], negative-energy states must be bound.  The [[energy spectrum]] of the set of bound states are most commonly discrete, unlike [[scattering state]]s of [[Free particle|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".<ref>{{cite book |last1=Sakurai |first1=Jun |editor1-last=Tuan |editor1-first=San |title=Modern Quantum Mechanics |date=1995 |publisher=Addison-Wesley |location=Reading, Mass |isbn=0-201-53929-2 |pages=418–9 |edition=Revised |chapter=7.8 |quote=Suppose the barrier were infinitely high ... we expect bound states, with energy ''E''&nbsp;>&nbsp;0. ... They are ''stationary'' states with infinite lifetime.  In the more realistic case of a finite barrier, the particle can be trapped inside, but it cannot be trapped forever.  Such a trapped state has a finite lifetime due to quantum-mechanical tunneling. ... Let us call such a state '''quasi-bound state''' because it would be an honest bound state if the barrier were infinitely high.}}</ref>  Examples include [[radionuclides]] and [[Rydberg atom]]s.<ref>{{Cite book |last=Gallagher |first=Thomas F. |url=https://www.cambridge.org/core/product/identifier/9780511524530/type/book |title=Rydberg Atoms |date=1994-09-15 |publisher=Cambridge University Press |isbn=978-0-521-38531-2 |edition=1 |pages=38–49 |chapter=Oscillator strengths and lifetimes |doi=10.1017/cbo9780511524530.005}}</ref>

In [[special relativity|relativistic]] [[quantum field theory]], a stable bound state of {{mvar|n}} particles with masses <math>\{m_k\}_{k=1}^n</math> corresponds to a [[pole (complex analysis)|pole]] in the [[S-matrix]] with a [[center of mass frame|center-of-mass energy]] less than <math>\textstyle\sum_k m_k</math>.  An [[unstable]] bound state shows up as a pole with a [[complex number|complex]] center-of-mass energy.