On the linear chain with arbitrary masses and force constants. I. Correlation functions

Simple expressions are derived for the time dependent correlation functions of certain phase functions of the classical linear (harmonic) chain having arbitrary masses and force constants. This is done for a statistical distribution τ (H, P) in phase space depending arbitrarily on the energy H and the total momentum P, which then is specialized to the uniform distributions τH, on the surface of constant energy, and τH,P, in the intersection of surfaces of constant energy and total momentum. In a subsequent paper2) the results will be used to draw conclusions on the ergodic properties of the phase functions.