2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/199002The nuclear collective response at finite temperature is investigated for the first time in the quantum framework of the small amplitude limit of the extended TDHF approach, including a non-Markovian collision term. It is shown that the collision width satisfies a secular equation. By employing a Skyrme force, the isoscalar monopole, isovector dipole and isoscalar quadrupole excitations in $^{40}Ca$ are calculated and important quantum features are pointed out. The collisional damping due to decay into incoherent 2p-2h states is small at low temperatures but increases rapidly at higher temperatures.22 Latex pages including 9 figures. Phys. Rev. C (in press)Nuclear Theorytext