  Integral representation for the eigenfunctions of quantum periodic Toda chain
is constructed for N-particle case. The multiple integral is calculated using
the Cauchy residue formula. This gives the representation which reproduces the
particular results obtained by Gutzwiller for N=2,3 and 4-particle chain. Our
method to solve the problem combines the ideas of Gutzwiller and R-matrix
approach of Sklyanin with the classical results in the theory of the Whittaker
functions. In particular, we calculate Sklyanin's invariant scalar product from
the Plancherel formula for the Whittaker functions derived by
Semenov-Tian-Shansky thus obtaining the natural interpretation of the Sklyanin
measure in terms of the Harish-Chandra function.
