  The diagonalization of the metrical and canonical Hamilton operators of a
scalar field with an arbitrary coupling, with a curvature in N-dimensional
homogeneous isotropic space is considered in this paper. The energy spectrum of
the corresponding quasiparticles is obtained and then the modified
energy-momentum tensor is constructed; the latter coincides with the metrical
energy-momentum tensor for conformal scalar field. Under the diagonalization of
corresponding Hamilton operator the energies of relevant particles of a
nonconformal field are equal to the oscillator frequencies, and the density of
such particles created in a nonstationary metric is finite. It is shown that
the modified Hamilton operator can be constructed as a canonical Hamilton
operator under the special choice of variables.
