Analytical Methods in Mesoscopic Systems

The propsect of designing technologies around the quantum behavior of mesoscopic devices is enticing. This thesis present several tools to facilitate the process of calculating and analyzing the quantum properties of such devices - resonance, boundary conditions, and the quantum-classical correspondence are major themes that we study with these tools. In Chapter 1, we begin by laying the groundwork for the tools that follow by defining the Hamiltonian, the Green's function, the scattering matrix, and the Landauer formalism for ballistic conduction.