Moments of energy level distributions in vibrational spectra

Expressions for moments of the spectral density distribution of a system described by a non-symmetric N-particle Hamiltonian are derived. In particular, this kind of Hamiltonian may represent N coupled oscillators; then its spectrum models the vibrational spectrum of a molecule. It is assumed that the Hamiltonian is defined in a finite-dimensional space formed by products of orthogonal eigenstates of some one-body Hamiltonians. Possible applications of the formalism are briefly discussed.