We studied a quantum-well state ͑QWS͒ generated by the adsorption of one monolayer of K on Cu͑111͒ surface by means of a first principles approach. We calculated the electronic properties of the system within the Inglesfield's embedding method, which enables us to investigate the elastic linewidth of surface states. Our findings are in good agreement with recent experimental results obtained from photoemission spectroscopy measurements for binding energy and k ʈ dispersion. We also studied the contributions to the QWS linewidth due to electron-electron many-body effects and electron-phonon scattering in Hedin's GW approach and within the Debye model, respectively. The main contribution to the linewidth is due to intraband transitions within the QWS itself, accounting for ϳ16 meV to the total width. The elastic, electron-phonon, and interband transition contributions are smaller than 3 meV each.