We report experiment and theory on the pressure dependence of quantum‐well bound states formed in the GaAs/AlxGa1−xAs heterostructure system. Using MQW’s and SL’s of various barrier compositions x, we trace in photoluminescence (8 K), and in full‐scale pseudopotential calculation, the pressure‐induced evolution of the lowest spatially confined states within the wells. With increasing pressure Γ‐confined states follow the shift to higher energies of the direct GaAs band gap. At critical pressures a crossing occurs between these Γ bound states and the barrier indirect X states. Here, Γ intensities plunge and new emission tracking the X edges appears. Confirmed in wave function calculation, these new transitions occur across the heterointerface, between X‐confined electrons within the AlxGa1−xAs and Γ‐confined holes within the GaAs. Arising from valence‐offset‐induced staggered band alignment, critical pressures for observation of these states decrease with increasing Al mole fraction. We thus obtain, with p...