If A and B are Hermitian operators, show that AB is Hermitian if and only if A commutes with B
Solution
Given that
A and B are Hermitian operators
So
"\\hat{A}^+=\\hat{A}\\\\\\hat{B}^+=\\hat{B}"
Then checking
"[A, B]^+=(AB-BA)^+\\\\=BA-AB\\\\=-(AB+BA)"
This is possible for
A commutes with B. So this is answer.
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