2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/102503We present a technique to resolve a Gaussian density matrix and its time evolution through known expectation values in position and momentum. Further we find the full spectrum of this density matrix and apply the technique to a chain of harmonic oscillators to find agreement with conformal field theory in this domain. We also observe that a non-conformal state has a divergent entanglement entropy.7 pages, 6 figuresQuantum Physicstext