Few problems in physics and engineering can be solved exactly, and one has to resort to approximate or numerical methods. Consider, for example, an electron in a square well whose potential is tilted by applying an electric field. The energy and wave function of its states change only slightly if the field is small. The lowest state becomes polarized to the deeper part of the well, causing a quadratic reduction in its energy. Perturbation theory provides a framework for calculating such changes, and this example is discussed in Section 7.2.
This approach works well if the potential can be divided into a ‘large’ part that can ...