The Tunneling Effect and Transport Properties
In this chapter we will solve the Schrödinger equation for simple one-dimensional examples. We will show that, despite the simple mathematical tools used to solve these systems exhibit important quantum properties like the energy quantization and the tunneling effect. The one-dimensional examples that we will consider here are: the step potential; the finite rectangular quantum well and the rectangular potential barrier. In these systems the potential functions are piecewise constant, with abrupt discontinuities at two or three points. For many years this kind of potentials were systems of academic interest and used to model real systems, where the mathematical procedures imply more involved calculations. In the current nano-structure physics, the rectangular quantum wells and the rectangular potential barriers are not any more systems of purely academic interest.