Bound state information

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.^[1]

In quantum physics, a bound state is a quantum state of a particle subject to a potential such that the particle has a tendency to remain localized in one or more regions of space.^[2] 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 vanishing at infinity, negative-energy states must be bound. The energy spectrum of the set of bound states are most commonly discrete, unlike scattering states of 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".^[3] Examples include radionuclides and Rydberg atoms.^[4]

In relativistic quantum field theory, a stable bound state of $n$ particles with masses $\{m_{k}\}_{k=1}^{n}$ corresponds to a pole in the S-matrix with a center-of-mass energy less than $\textstyle \sum _{k}m_{k}$ . An unstable bound state shows up as a pole with a complex center-of-mass energy.

^ "Bound state - Oxford Reference".
^ Blanchard, Philippe; Brüning, Erwin (2015). Mathematical Methods in Physics. Birkhäuser. p. 430. ISBN 978-3-319-14044-5.
^ Sakurai, Jun (1995). "7.8". In Tuan, San (ed.). Modern Quantum Mechanics (Revised ed.). Reading, Mass: Addison-Wesley. pp. 418–9. ISBN 0-201-53929-2. Suppose the barrier were infinitely high ... we expect bound states, with energy E > 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.
^ Gallagher, Thomas F. (1994-09-15). "Oscillator strengths and lifetimes". Rydberg Atoms (1 ed.). Cambridge University Press. pp. 38–49. doi:10.1017/cbo9780511524530.005. ISBN 978-0-521-38531-2.

[1] "Bound state - Oxford Reference".

[2] Blanchard, Philippe; Brüning, Erwin (2015). Mathematical Methods in Physics. Birkhäuser. p. 430. ISBN 978-3-319-14044-5.

[3] Sakurai, Jun (1995). "7.8". In Tuan, San (ed.). Modern Quantum Mechanics (Revised ed.). Reading, Mass: Addison-Wesley. pp. 418–9. ISBN 0-201-53929-2. Suppose the barrier were infinitely high ... we expect bound states, with energy E > 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.

[4] Gallagher, Thomas F. (1994-09-15). "Oscillator strengths and lifetimes". Rydberg Atoms (1 ed.). Cambridge University Press. pp. 38–49. doi:10.1017/cbo9780511524530.005. ISBN 978-0-521-38531-2.

Bound state information

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