The quantum-mechanical theory for Mossbauer spectroscopy using a resonant detector, in which the con version electrons are recorded, is presented. The resonant detector consists of nuclei having the same microscopic environment as the source nuclei. Fundamental equations, in the frequency domain, describing the system formed by a source nucleus, an ensemble of absorber nuclei, and a resonant detector nucleus are solved. the absorber is allowed to be of arbitrary thickness. The analysis includes the presence of conversion electrons and gamma radiation. The full width at half maximum of a Mossbauer spectrum, using the resonant-detector scheme is calculated and found to be appreciably smaller than the width found using a conventional Mossbauer setup.