Discrete peaks, due to the excited 2S state of the n=l symmetric heavy hole (hh) exciton, are observed in the photoluminescence excitation spectra of GaAs/AlGaAs coupled double quantum well (CDQW) samples. The observations of the 2S state allow a precise determination of 1S-2S splitting, and the experimental results show a good agreement with a simple calculation which is based on a model of fractional-dimension of the exciton state. The obtained values for the 1S-2S splitting are significantly reduced compared with the corresponding single (or multiple) quantum wells (QW). Central acceptors confined in CDQWs have also been studied. Due to built in electric fields, interwell and intrawell excitons bound to neutral acceptors are simultaneously observed in weakly coupled doped double QWs. The diamagnetic shift and binding energy of the bound excitons are similar to results of the single QW’s, while the diamagnetic shift of the free exciton differs from single QW’s.