The spectral autocorrelation for a set of over 400 near-field photoluminescence spectra of a narrow quantum well has been evaluated. It is compared with a microscopic model of an exciton in a disorder potential. The analysis provides strong evidence for quantum mechanical level repulsion and allows a quantitative estimate of the microscopic disorder features. The concept of participation ratio is invoked to quantify the exciton center-of-mass localization lengths. These turn out to be broadly distributed and increase rapidly with energy.