If Acirc and BHat are both Hermitian which of the following

If Acirc and B^Hat are both Hermitian, which of the following three operators are Hermitian? i(Acirc B^Hat - B^Hat Acirc). (Acirc B^Hat - B^Hat Acirc). (Acirc B^Hat + B^Hat Acirc/2).

Solution

option c

(AB+BA/2)+ - (AB+BA/2) = BA + AB/2 - AB - BA/2 = BA/2 - AB/2 = [B,A] / 2 So if A and B do not commute, the difference between your operator and its conjugate is not 0 (because equal to the commutator divided by 2).
And if operator A corresponds to observable A, and operator B corresponds to observable B, what is a \"good\" (i.e.Hermitian) operator that corresponds to the physically observable product AB

1/2 (AB + BA).