 Solution

ID: past-exam-of-the-mathematical-methods-i-course-of-the-university-of-oxford/2019-resit/11/a/iii/solution

Taking the Hermitian adjoint reverses the products and leaves their sum unchanged:

(\frac{A B + B A}{2})^{†} = \frac{B A + A B}{2} .

Thus the symmetrized product is Hermitian, whether or not

A

and

B

commute. This is the Hermitian anticommutator divided by two.

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