Quantum Coherence and Energy Levels Splitting

Abstract

In the previous chapter we solved the Schrödinger equations for the potential barrier and the quantum well. These important and soluble systems, revealed fundamental properties present in the actual quantum systems. Some of the results obtained for these systems will reappear, in this and the coming chapters, and will enhance the insight into the quantum phenomena and their physical meaning. In this chapter we will study systems with slightly more complex structure, but still piecewise constant potentials. We will begin with the double quantum well with infinite walls, and we will continue with the double potential barrier and the double quantum well with finite lateral walls. In these systems a new phenomenon will appear: the splitting of the energy levels. We will conclude this chapter with a brief introduction to the finite periodic systems theory, applied to the Kronig–Penney model, taken as a finite sequence of rectangular wells and barriers. We will see that the energy levels splitting is responsible for the formation of energy bands, an essential property closely related to the quantum phase coherence, that makes it possible for us to see fundamental differences in the physical behavior of metals, semiconductors and insulators.