Although no particle truly exists in a box having infinite walls, the particle-
in-a-box illustrates all of the important aspects of quantum mechanics: satis-
fying the Schrödinger equation, normalization, orthogonality, quantized en-
ergy values, degeneracy. All other systems, real and ideal, also have these
properties. We will continue the application of quantum mechanics to other
ideal and real systems in the next chapter, where we will assume that the reader
is familiar with these topics. If you are not, review the material in this chapter.
It contains all of the preliminary background necessary to apply the quantum
mechanical theory of atoms and molecules to any system, from the ideal par-
ticle-in-a-box to a DNA molecule. Although some new concepts will be pre-
sented in the following chapters, most of the basic components of quantum
mechanics have already been covered. Any discussion of quantum mechanics
is fundamentally based on the material in this chapter.310 CHAPTER 10 Introduction to Quantum Mechanics