Answer to Question #282974 in Quantum Mechanics for BIGIRIMANA Elie

Question

Let A and B be two non-commuting Hermitian operators. Determine

which of the following operators are Hermitians:

(a) AB

(b) [A, B]

(c) {A, B} = AB + BA

(d) ABA

(e) An where n is an integer.

Answer 1

Solution

Any operator A said to hermitian

When

$\hat{A}=\hat{A}^+$ ...........(1)

Now checking

Operator ABA

$(ABA) ^+=A^+B^+A^+$

=$ABA$

Which follow essential conditions for hermitian.

So option d is hermitian and all others are not hermitian.