A mathematical proof of the indistinguishability of permutations in the same N.M.R. mode

Abstract

Klemperer has argued that rearrangements belonging to the same double coset HxH give rise to identical N.M.R. line shapes. This result rests on the assumption that, when a given effective spin hamiltonian is associated with each molecular configuration, rearrangements corresponding to identical switches of effective spin hamiltonians must give rise to identical line shapes.

Since the explicit relation between this assumption and an analytical expression for the N.M.R. line shape has never been established, we derive Klemperer's result by starting from N.M.R. line-shape expressions instead of using his assumption.