Observed spatial- and frequency-domain signatures of the most intense solar wind Langmuir waves can be described as localized, discrete-frequency eigenmodes trapped in a parabolic density fluctuation. Electric field waveforms from spacecraft in the solar wind are compared with one- and three-dimensional solutions and, in many cases, can be represented by 1-3 of the lowest order eigenmodes. The spatial scale of eigenmode wave packets is on the order of tens of Langmuir wavelengths, allowing them to draw energy directly from the unstable electron distributions associated with a solar type III radio bursts and implying that Langmuir waves can grow in a strongly inhomogeneous medium. The currents generated by localized Langmuir eigenmodes emit coherent electromagnetic radiation as antennas at the fundamental and at twice the local plasma frequency. STEREO observations demonstrate that the currents required for eigenmode antenna radiation are present and have strengths within an order of magnitude of theoretical predictions. The eigenmode antenna radiation mechanism implies that, of all the Langmuir waves excited by an electron beam, relatively few localized antenna radiators may account for a majority of observed emission from an extended radio source. Finally, the possibility that turbulence may ultimately play a strong role in the generation of Langmuir waves and the radio emissions associated with solar type II and type III radio bursts is investigated.