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 group unitary operator of formula_103 that commutes with them is an formula_121 multiplier. But commuting with translations implies that the multiplier is constant. A version of the Stone–von Neumann theorem, proved by George Mackey, holds for the Heisenberg group formula_113. The Fourier transform is the unique intertwiner between the representations of formula_103 and formula_124. See the discussion at Stone–von Neumann theorem#Relation to the Fourier transform for details. Heisenberg group In mathematics, the Heisenberg group formula_1, named after Werner Heisenberg, is the group of 3×3 upper triangular matrices of the form under the operation of matrix multiplication. Elements "a, b" and "c"