Quantum Mechanics: Concepts and Applications · Problem 2.6
Mathematical Tools of Quantum Mechanics — Nouredine Zettili
Physics — Quantum Mechanics · hermitian-operators
Problem
(a) Discuss the hermiticity of the operators (A^+A^†), i(A^+A^†), and i(A^−A^†).
(b) Find the Hermitian adjoint of f(A^)=(1+iA^+3A^2)(1−2iA^−9A^2)/(5+7A^).
(c) Show that the expectation value of a Hermitian operator is real and that of an anti-Hermitian operator is imaginary.