of the wider quantum well a is lower than the energy e b of the narrower quantum well b next an electric field is applied to the quantum wells in the direction from b to a as illustrated in fig6 b in this case as for the electron system the energy of the well a increases and the energy of the well b decreases so that a resonant condition is obtained in which the electron energy levels of the two quantum wells agree with each other in this case as illustrated in fig6 b the wave functions of the electrons vary to two coupled states u2014 a symmetric state low energy coupled state and an anti symmetric state high energy coupled state the wave functions of the coupled states are characterized by extending across the two quantum wells unlocalized so that they are not localized in one well in contrast the hole energy levels shift in the opposite direction to the electron energy levels so that the energy difference between the quantum wells a and b increases in this case since the holes do not make resonant coupling between the two quantum wells they are localized in one well each in this case a state in which an exciton which consist of a hole in the quantum well a and an electron in the symmetric coupled state extending across the wells a and b are excited is designated by 1 gt a and a state in which the excitons are not excited is designated by 0 gt a likewise a state in which the excitons which consist of.