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The resulting stationary states and scattering properties of an effectivepotential brought about by embedding a quantum well in another well areinvestigated in this work. The composite well system is constructed via asuperposition of modified Poeschl - Teller potential wells. The energy spectrumin each composite well is obtained using the shooting method and the transportof 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 theground state energy of the well-in-a-well system. Moreover, the bound statesincrease in number and become more evenly spaced. In addition, the transmissionprobability of a free particle incident above a composite well is lowest forthe system with a large embedded well as compared to well-in-a-well systems ofthe same depth. Small variations in designed potential wells yield differentquantum mechanical features.

Tailor-made Quantum Well-in-a-Well Systems: Their Bound States and Scattering Properties