Localized Langmuir waves are commonly observed in space plasmas and are a potential source of radio waves. Using electric field data from STEREO, it is shown that these localized Langmuir waves are eigenmodes of density wells estimated independently. An analytic model is developed for the eigenmode frequencies. The inferred depths and widths of the density wells typically only allow the zeroth-order Langmuir eigenmode to form, explaining the preponderance of single-peaked waveforms. More complicated waveforms are shown to be consistent with single eigenmode solutions of more complicated density profiles. The inferred depth of the density well increases with Langmuir wave intensity, consistent with the ponderomotive force but not wave packet collapse.