Answer to Question #282978 in Quantum Mechanics for BIGIRIMANA Elie

Question #282978

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



only if A commutes with B

1
Expert's answer
2022-02-09T09:15:07-0500

Solution


Given that


A and B are Hermitian operators

A^+=A^B^+=B^\hat{A}^+=\hat{A}\\\hat{B}^+=\hat{B}

So we check

[A,B]+=(ABBA)+=BAAB=(AB+BA)[A, B]^+=(AB-BA)^+\\=BA-AB\\=-(AB+BA)

This is possible for


A commutes with B. So this is answer.




So


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