Problem 3.3 – Griffith’s Intro to QM

Problem 3.3

Show that if $\langle h| \hat{Q} h \rangle = \langle \hat{Q} h|h \rangle$ for all h (in Hilbert space), then $\langle f| \hat{Q} g \rangle = \langle \hat{Q} f|g \rangle$ for all f and g (i.e. the two definitions of “hermitian”—Equations 3.16 and 3.17—are equivalent). Hint: First let $h=f+g$ , and then let $h=f+ig$ .