2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/45716We propose an non-standard method to calculate non-equilibrium physical observables. Considering the generic example of an anharmonic quantum oscillator, we take advantage of the fact that the commutator algebra of second order polynomials in creation/annihilation operators closes. We solve the von~Neumann equation for the density-operator exactly in the mean field approximation and study the time evolution of the particle number and the expectation value < X^2 > .6 pages, REVTeX, no figuresHigh Energy Physics - Phenomenologytext