Tailor-made Quantum Well-in-a-Well Systems: Their Bound States and   Scattering Properties
  The resulting stationary states and scattering properties of an effective potential brought about by embedding a quantum well in another well are investigated in this work. The composite well system is constructed via a superposition of modified Poeschl - Teller potential wells. The energy spectrum in each composite well is obtained using the shooting method and the transport of a particle above this system is analyzed using the transfer matrix method. It is shown that decreasing the size of the embedded middle well lowers the ground state energy of the well-in-a-well system. Moreover, the bound states increase in number and become more evenly spaced. In addition, the transmission probability of a free particle incident above a composite well is lowest for the system with a large embedded well as compared to well-in-a-well systems of the same depth. Small variations in designed potential wells yield different quantum mechanical features. 
Naomi Jane Jacosalem and Cristine Villagonzalo