Let’s see how this formalism works in an explicit example. Let’s consider a potential that is the infinite square well that has a little bump in the center, as shown in Fig. 10.1. That is, the potential is

The Schrödinger equation in position space is then

where Θ(x) is called the Heaviside theta function and is defined to be

We can then identify the little bump as our perturbation potential:

and let’s see how the ground state of the well is affected by the bump.

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