Answer to Question #282975 in Quantum Mechanics for BIGIRIMANA Elie

Question #282975

 If A and B are Hermitian operators, show that AB is Hermitian if and only if A commutes with B


1
Expert's answer
2022-02-07T15:31:07-0500

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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