Kramers–Heisenberg formula Kramers–Heisenberg formula The Kramers–Heisenberg dispersion formula is an expression for the cross section for scattering of a photon by an atomic electron. It was derived before the advent of quantum mechanics by Hendrik Kramers and Werner Heisenberg in 1925, based on the correspondence principle applied to the classical dispersion formula for light. The quantum mechanical derivation was given by Paul Dirac in 1927. The Kramers–Heisenberg formula was an important achievement when it was published, explaining the notion of "negative absorption" (stimulated emission), the Thomas–Reiche–Kuhn sum rule, and inelastic scattering — where the energy of the scattered photon may be larger
Heisenberg model (quantum) Assuming that there's only one critical point, we can conclude that the phase transition happens at formula_22. It is common to name the model depending on the values of formula_23, formula_24 and formula_6: if formula_26, the model is called the Heisenberg XYZ model; in the case of formula_27, it is the Heisenberg XXZ model; if formula_28, it is the Heisenberg XXX model. The spin 1/2 Heisenberg model in one dimension may be solved exactly using the Bethe ansatz. In the algebraic formulation, these are related to particular Quantum affine algebras and Elliptic Quantum Group in the XXZ and XYZ cases