Show that if (h|h) = (hh) for all functions h (in Hilbert space), then (flg) =...

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Show that if (h|Ôh) = (Ôh\h) for all functions h (in Hilbert space), then (flÔg) = (ôflg) for all f and g (i.e., the two definitions of "hermi- tian"-Equations 3.16 and 3.17-are equivalent). Hint: First let h = f+ 8, and then let h = f +ig. (SIÊF) = (ÔFIS) for all f(x). [3.16] (FIÔg) = (Ô ƒ\g) for all f(x) and all g(x). [3.17] Show that if (h|Ôh) = (Ôh\h) for all functions h (in Hilbert space), then (flÔg) = (ôflg) for all f and g (i.e., the two definitions of "hermi- tian"-Equations 3.16 and 3.17-are equivalent). Hint: First let h = f+ 8, and then let h = f +ig. (SIÊF) = (ÔFIS) for all f(x). [3.16] (FIÔg) = (Ô ƒ\g) for all f(x) and all g(x). [3.17]