The tunability of the states of two coupled parabolic quantum wells subjected to an electric field is studied by using the transfer-matrix approach. Two numerical procedures are used. Both involve subdividing the potential profile into a number of linear or step partitions. For the linear partition approach, the Airy function solution of the Schrödinger equation is employed while for the step approach, the plane-wave solution is used. Both methods give identical results if small enough partition intervals are used. It is found that the plane-wave method is easier and that it simplifies the programming without seriously sacrificing the calculational speed. The coupled well width, the barrier width, and the applied field were changed systematically to study the changes in the energy levels, wave functions, and transmission of a resonant tunneling diode based on the double parabolic structure. The anticrossing between the energy levels on changing the well width or the bias of the coupled wells is seen and discussed. It is also found that the transmission peak is sharp and deep if the resonance occurs in both of the coupled wells at the same energy, while it is smaller and broader if the resonance occurs in only one well because the wave function is blocked by the other nonresonant well.