Show that if (h|Qh) = (Ôh\h) for all functions h (in Hilbert space), then (flQg) = (Ôƒ[g) 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] (SIêg) = (Ô ƒlx) for all f(x) and all g(x). [3.17] %3D
Show that if (h|Qh) = (Ôh\h) for all functions h (in Hilbert space), then (flQg) = (Ôƒ[g) 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] (SIêg) = (Ô ƒlx) for all f(x) and all g(x). [3.17] %3D
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![Show that if (h|ệh) = (Ôh\h) for all functions h (in Hilbert space),
then (flÔg) = (Ôf\g) 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) = (Ô ƒIS) for all f(x).
[3.16]
(FIÔg) = (Ô ƒ\g) for all f (x) and all g(x).
[3.17]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8f84f05b-74a4-4ecd-80d5-92a98a952538%2Fd8cf95c4-ded2-4c1e-a0e6-e67e5fe8ba02%2Fs24pwcxb_processed.png&w=3840&q=75)
Transcribed Image Text:Show that if (h|ệh) = (Ôh\h) for all functions h (in Hilbert space),
then (flÔg) = (Ôf\g) 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) = (Ô ƒIS) for all f(x).
[3.16]
(FIÔg) = (Ô ƒ\g) for all f (x) and all g(x).
[3.17]
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