Spatially resolved photoluminescence spectra of a single quantum well are recorded by near-field spectroscopy. A set of over four hundred spectra displaying sharp emission lines from localized excitons is subject to a statistical analysis of the two-energy autocorrelation function. An accurate comparison with a quantum theory of the exciton center-of-mass motion in a two-dimensional spatially correlated disordered potential reveals clear signatures of quantum mechanical energy level repulsion, giving the spatial and energetic correlations of excitons in disordered quantum systems.