  The quantum separation of variables method consists in mapping the original
Hilbert space where a spectral problem is formulated onto one where the
spectral problem takes a simpler "separated" form. In order to realise such a
program, one should construct the map explicitly and then show that it is
unitary.
  In the present paper, we develop a technique which allows one to prove the
unitarity of this map in the case of the quantum Toda chain. Our proof solely
builds on objects and relations naturally arising in the framework of the
so-called quantum inverse scattering method. Hence, with minor modifications,
it should be readily transposable to other quantum integrable models solvable
by the quantum separation of variables method. As such, it provides an
important alternative to the proof of the map's unitarity based on the group
theoretical interpretation of the quantum Toda chain, which is absent for more
complex quantum integrable models.
