The heat current across a quantum harmonic system connected to reservoirs at
different temperatures is given by the Landauer formula, in terms of an
integral over phonon frequencies \omega, of the energy transmittance T(\omega).
There are several different ways to derive this formula, for example using the
Keldysh approach or the Langevin equation approach. The energy transmittance
T({\omega}) is usually expressed in terms of nonequilibrium phonon Green's
function and it is expected that it is related to the transmission coefficient
{\tau}({\omega}) of plane waves across the system. In this paper, for a
one-dimensional set-up of a finite harmonic chain connected to reservoirs which
are also semi-infinite harmonic chains, we present a simple and direct
demonstration of the relation between T({\omega}) and {\tau}({\omega}). Our
approach is easily extendable to the case where both system and reservoirs are
in higher dimensions and have arbitrary geometries, in which case the meaning
of {\tau} and its relation to T are more non-trivial.Comment: 17 pages, 1 figur
