Bethe ansatz

In physics, the Bethe ansatz is used to calculate the exact wave functions of certain quantum-mechanical many-body systems, most commonly in one spatial dimension. This ansatz was introduced by Hans Bethe in 1931 to obtain the exact eigenvalues and eigenvectors of the one-dimensional antiferromagnetic isotropic (XXX) Heisenberg model.

The approach was later generalized into the quantum inverse scattering method (QISM) and the algebraic Bethe ansatz, forming the basis of modern integrable system theory.

Since then, the method has been extended to other spin chains, statistical lattice models and generalized hydrodynamics.

"Bethe ansatz problems" were one of the topics featuring in the "To learn" section of Richard Feynman's blackboard at the time of his death.

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