Aspects of the Modeling of Low Dimensional Quantum Systems

Abstract

The mathematical modeling of low dimensional quantum systems is discussed in this chapter. In particular, the use of generalized functions in such modeling is illustrated in some detail, including applications of the Dirac delta function and its derivative (“delta-prime”) in determining quantum mechanical Schrödinger Green’s functions describing the dynamics of various low dimensional systems. The illustrations include quantum dots, wires and wells (and a superlattice) in various dimensions. Also, the one-dimensional “delta-prime” potential is shown to provide an impenetrable barrier.