Abstract A harmonic oscillator weakly coupled to a heat bath is studied without invoking the rotating wave approximation. Correction to the lorentzian lineshape which characterizes the RWA are derived. An expression for the time evolution of the population of the oscillator which is exact in the van Hove weak coupling limit is also obtained. Our results are compared to earlier expressions which were obtained using the rotating wave approximation. p ]In our equation for the population of the oscillator, we observe an additional transient term, and we examine the time evolution of the population under a variety of conditions. The applicability of the rotating wave approximation is discussed in light of our results.