Nano-science is one of the fastest growing fields in both physics and engineering. It is now possible to design and fabricate devices whose physical dimensions are on the nanometer scale and whose quantum properties can be tuned as desired.  In this notebook we will study the quantum mechanics of what are known as reduced dimensional structures.  A structure is said to have reduced dimensionality if one or more of the dimensions is on the order of the De Broglie wavelength of the particles confined to the structure. An ordinary wire for example, has no reduced dimensionality since both its length and its radius are large compared to the De Broglie wavelength of room temperature electrons.