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The emission of visible light is observed from the metallic quantum well system Na on Cu(111) when electrons tunnel from the tip of a scanning tunnelling microscope to an unoccupied state of the sample. Spectral analysis of the emission along with tunnelling spectroscopy is used to show that the emission is comprised of two components. A sharp spectral feature is found to be due to an interband transition between quantum well states of the Na layer. The other component is similar to plasmon-mediated emission observed previously from clean metal surfaces. The results suggest that light emission is a unique local probe of the electronic structure of quantum well systems.