Consider a particle in the potential shown in Figure 7.3.
(a) Find the first-order correction to the ground-state wave function. The first three nonzero terms in the sum will suffice.
(b) Using the method of Problem 2.61 find (numerically) the ground-state wave function and energy. Use V₀ = 4ћ² / ma² and N = 100. Compare the energy obtained numerically to the result from first-order perturbation theory (see Example 7.1).
(c) Make a single plot showing (i) The unperturbed ground-state wave function, (ii) The numerical ground-state wave function, and (ii) The first-order approximation to the ground-state wave function.

Example 7.1

N 1 = y(x) dx ~ 1 Ax. / = i=1