Problem 3.5 – Griffith’s Intro to QM

Problem 3.5

(a) Find the hermitian conjugates of x, i, and $d/dx$ .
(b) Show that $(\hat{Q} \hat{R})^{\dag} = \hat{R}^{\dag} \hat{Q}^{\dag}$ (note the reversed order), $(\hat{Q} + \hat{R})^{\dag} = \hat{Q}^{\dag} + \hat{R}^{\dag}$ and $(c \hat{Q})^{\dag} = c^* \hat{Q}^{\dag}$ for a complex number c.
(c) Construct the hermitian conjugate of $a_+$ (Equation 2.48).