Ullersma's model consistently describes the quantum-mechanical damped harmonic oscillator. Proper limiting processes in the initially reversible solutions lead to irreversible behavior. It is shown that the irreversible solutions can directly be derived from a field version of the discrete Ullersma Hamiltonian H (H\ensuremath{\rightarrow}
HF). In the ground state of the system the phonon occupation number of the oscillator does not vanish. Therefore, these ``bare'' phonons cannot be interpreted as ``physical'' quanta or particles. By suitable canonical transformations, the bare-field description is transformed into a physical description (
HF\ensuremath{\rightarrow}
Hph), which allows the definition of physical particles and which is characterized by a renormalized frequency, a screened interaction between oscillator and bath, and a symmetry of position and momentum operators. The physical description is closely related to the rotating-wave approximation of the original model. The relaxation behavior and the equilibrium properties of the different descriptions are discussed and compared.