(a) Show that the set of all square-integrable functions is a vector space (refer to Section A.l for the definition). Hint: The main problem is to show that the sum of two square-integrable functions is itself square-integrable. Use Equation 3.7. Is the set of all normalized functions a vector space?
(b) Show that the integral in Equation 3.6 satisfies the conditions for an inner product (Section A.2).
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