We show that sharp nonmonotic variation of low temperature electron mobility μ can be achieved in GaAs/AlxGa1-xAs barrier delta-doped double quantum well structure due to quantum mechanical transfer of subband electron wave functions within the wells. We vary the potential profile of the coupled structure as a function of the doping concentration in order to bring the subbands into resonance such that the subband energy levels anticross and the eigen states of the coupled structure equally share both the wells thereby giving rise to a dip in mobility. When the wells are of equal widths, the dip in mobility occurs under symmetric doping of the side barriers. In case of unequal well widths, the resonance can be obtained by suitable asymmetric variation of the doping concentrations. The dip in mobility becomes sharp and also the wavy nature of mobility takes a rectangular shape by increasing the barrier width. We show that the dip in mobility at resonance is governed by the interface roughness scattering through step like changes in the subband mobilities. It is also gratifying to show that the drop in mobility at the onset of occupation of second subband is substantially supressed through the quantum mechanical transfer of subband wave functions between the wells. Our results can be utilized for performance enhancement of coupled quantum well devices.