In a recent paper we showed the equivalence, under certain well-characterized assumptions, of Redfield’s equations for the density operator in the energy representation with the Gaussian phase space ansatz for the Wigner function of Yan and Mukamel. The equivalence shows that the solutions of Redfield’s equations respect a striking degree of classical-quantum correspondence. Here we use this equivalence to derive analytic expressions for the density matrix of the harmonic oscillator in the energy representation without making the almost ubiquitous secular approximation. From the elements of the density matrix in the energy representation we derive analytic expressions for Γ1n(1/T1n) and Γ2nm(1/T2nm), i.e., population and phase relaxation rates for individual matrix elements in the energy representation. Our results show that Γ1n(t)=Γ1(t) is independent of n; this is contrary to the widely held belief that Γ1n is proportional to n. We also derive the simple result that Γ2nm(t)=|n−m|Γ1(t)/2, a generalization of the two-level system result Γ2=Γ1/2. We show that Γ1(t) is the classical rate of energy relaxation, which has periodic modulations characteristic of the classical damped oscillator; averaged over a period Γ1(t) is directly proportional to the classical friction, γ. An additional element of classical-quantum correspondence concerns the time rate of change of the phase of the off diagonal elements of the density matrix, ωnm, a quantity which has received little attention previously. We find that ωnm is time-dependent, and equal to |n−m|Ω(t), where Ω(t) is the rate of change of phase space angle in the classical damped harmonic oscillator. Finally, expressions for a collective Γ1(t) and Γ2(t) are derived, and shown to satisfy the relationship Γ2=Γ1/2. This familiar result, when applied to these collective rate constants, is seen to have a simple geometrical interpretation in phase space.