Quantized atom-field dynamics in unstable cavities

We develop a quantum description for the dynamics of a single atom inside a n unstable optical resonator. For spherical mirrors with a finite Gaussian aperture we find a discrete complete set of normalizable eigenmodes, their biorthogonal adjoint modes, eigenfrequencies, decay rates, and overlap inte grals. With these modes we formulate a quantum description for the coupled dynamics of the field and a single atom inside the resonator. We find a str ongly geometry and position dependent nonexponential decay probability. Und er certain special conditions one gets a modified single-mode description i ncorporating the Petermann excess noise factor K even on a single-atom leve l.