Equation (4-21) expresses a function ψ(x) as a sum of plane waves, each with a coefficient A(k). Equation (4-22) finds the coefficients from the given function ψ(x). The equations aren’t independent statements; in fact, one is the. inverse of the other. Equation (4-22) gives A(k) when ψ(x) is known, and (4-21) does the reverse. Example 4.7 calculates A(k) from a specific ψ(x) Show that when this A(k) is inserted into (4-21),. the original is returned. Use the Euler formula and the symmetry properties of odd and even functions to simplify your work. (Nonetheless, you will probably have to look up the final integral in a table of integrals.)
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