••• (Section 11.4) To illustrate the property (11.20) of completeness, consider an infinite square well of width a = 1, centered on the origin, with stationary-state wave functions Ψn(x) as given in (11.34) and (11.35). Let Ψ(x) be the flat wave function equal to 1 everywhere inside the well (and 0 outside), (a) Find the coefficients Am in the expansion (11.20) of Ψ(x). (b) To reproduce Ψ(x) exactly, you would have to include all of the terms in the infinite series (11.20), but you can get a surprisingly good approximation by including just the first few terms. Use a suitable plotting program to plot the sum of the first 5 nonzero terms of the series, (c) Repeat with the first 10 nonzero terms.
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