A lot of features connected with absorption and emission of light in nanocrystals can be understood in terms of the quantum confinement approach. In this approach, a nanocrystal is considered as a three-dimensional potential box in which photon absorption and emission result either in a creation or in an annihilation of some elementary excitations in an electron subsystem. These excitations are described in terms of quasiparticles known for bulk crystals, that is, electrons, holes, and excitons.

This chapter is meant to remind readers of some principal results from elementary quantum mechanics and to provide an elementary introduction to solid state physics, which is essential for the following chapters. We then depart from elementary “particle-in-a-box” problems and consider the properties of an electron in a periodic potential. In the next step, we introduce the concepts of effective mass and quasiparticles as elementary excitations of a many-body system. Finally, we give an idea of the low-dimensional structures that constitute, undoubtedly, one of the major fields of research in modern condensed-matter physics.

A few problems from elementary quantum mechanics

Particle in a potential well

To restate some basic properties of quantum particles that are necessary to consider electrons in a crystal, we start with a particle in a one-dimensional potential well (Fig. 1.1).