# Scattering channel

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In [scattering theory](/source/Scattering_theory), a **scattering channel** is a [quantum state](/source/Quantum_state) of the colliding system before or after the collision (t \to \pm \infty).[1] The [Hilbert space](/source/Hilbert_space) spanned by the states before collision (in states) is equal to the space spanned by the states after collision (out states) which are both [Fock spaces](/source/Fock_space) if there is a [mass gap](/source/Mass_gap). This is the reason why the [S matrix](/source/S_matrix) which maps the in states onto the out states must be [unitary](/source/Unitary_operator). The scattering channel are also called scattering [asymptotes](/source/Asymptote). The Møller operators are mapping the scattering channels onto the corresponding states which are solution of the [Schrödinger equation](/source/Schr%C3%B6dinger_equation) taking the [interaction](/source/Fundamental_interaction) [Hamiltonian](/source/Hamiltonian_(quantum_mechanics)) into account.[2] The Møller operators are [isometric](/source/Isometry).

## References

1. Nesbet, Robert K. (2013-11-21). [*Variational Methods in Electron-Atom Scattering Theory*](https://www.google.co.uk/books/edition/Variational_Methods_in_Electron_Atom_Sca/OkH2BwAAQBAJ?hl=en&gbpv=1&dq=%2522Scattering+channel%2522+-wikipedia&pg=PA227&printsec=frontcover). Springer Science & Business Media. p. 2. ISBN 978-1-4684-8431-1. Retrieved 2025-07-22.

1. Gérard, Christian & Łaba, Izabella (2002). [*Multiparticle Quantum Scattering in Constant Magnetic Fields*](https://www.google.co.uk/books/edition/Multiparticle_Quantum_Scattering_in_Cons/GvzyBwAAQBAJ?hl=en&gbpv=1&dq=%2522Scattering+channel%2522+-wikipedia&pg=PA8&printsec=frontcover). American Mathematical Soc. ISBN 978-0-8218-2919-6. Retrieved 2025-07-22.

## See also

- [LSZ formalism](/source/LSZ_formalism)

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