  We extend a recent result of [13] for the KdV hierarchy to the Toda lattice
hierarchy. Namely, for an arbitrary solution to the Toda lattice hierarchy, we
define a pair of wave functions, and use them to give explicit formulae for the
generating series of $k$-point correlation functions of the solution.
Applications to computing GUE correlators and Gromov--Witten invariants of the
Riemann sphere are under consideration.
