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Quantum inverse scattering method
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<p>In <a href="/facts/Quantum_physics/BRc3Mzgr">quantum physics</a>, the quantum inverse scattering method (QISM), similar to the closely related algebraic Bethe ansatz, is a method for solving <a href="/facts/Integrable_system/Crgzjw6G">integrable models</a> in 1+1 dimensions, introduced by <a href="/facts/Leon_Takhtajan/WeaPaYot">Leon Takhtajan</a> and <a href="/facts/Ludvig_Faddeev/gR8t21SP">L. D. Faddeev</a> in 1979. </p><p>It can be viewed as a quantized version of the classical <a href="/facts/Inverse_scattering_method/CJ5dfzXJ">inverse scattering method</a> pioneered by <a href="/facts/Norman_Zabusky/K5HjNuHF">Norman Zabusky</a> and <a href="/facts/Martin_Kruskal/XJDpvkrC">Martin Kruskal</a> used to investigate the <a href="/facts/Korteweg%25E2%2580%2593de_Vries_equation/w8W3YDRK">Korteweg–de Vries equation</a> and later other <a href="/facts/Integrable_system/Crgzjw6G">integrable</a> <a href="/facts/Partial_differential_equations/DyPsBlv7">partial differential equations</a>. In both, a <a href="/facts/Lax_matrix/dyzB7Ttb">Lax matrix</a> features heavily and <a href="/facts/Scattering/nMou7lEH">scattering data</a> is used to construct solutions to the original system. </p><p>While the classical inverse scattering method is used to solve integrable partial differential equations which model <a href="/facts/Continuous_media/vI7LpFDk">continuous media</a> (for example, the KdV equation models shallow water waves), the QISM is used to solve <a href="/facts/Many-body_problem/n2rIxgwv">many-body</a> quantum systems, sometimes known as <a href="/facts/Spin_chain/kVl0Xll4">spin chains</a>, of which the <a href="/facts/Heisenberg_spin_chain/8RPu8n5n">Heisenberg spin chain</a> is the best-studied and most famous example. These are typically discrete systems, with particles fixed at different points of a lattice, but limits of results obtained by the QISM can give predictions even for <a href="/facts/Quantum_field_theory/VoewsNJV">field theories</a> defined on a continuum, such as the quantum <a href="/facts/Sine-Gordon_model/Ypbhz5tl">sine-Gordon model</a>. </p>