Читать книгу Quantum Mechanical Foundations of Molecular Spectroscopy - Max Diem - Страница 23

Real quantum mechanical systems have the tendency to become mathematically quite complicated due to the complexity of the differential equations introduced in the previous section. Thus, a simple model system will be presented here to illustrate the principles of quantum mechanics introduced in Sections 2.1 and 2.2. The model system to be presented is the so‐called particle in a box (henceforth referred to as “PiB”) in which the potential energy expression is simplified but still has with wide‐ranging analogies to real systems. This model is very instructive, since it shows in detail how the quantum mechanical formalism works in a situation that is sufficiently simple to carry out the calculations step by step while providing results that much resemble the results in a more realistic model. This is exemplified by the overall similarity such as the symmetry (parity) of the PiB wavefunctions when compared with that of the harmonic oscillator wavefunctions discussed in Chapter 4.