Problem 3.5 The hermitian conjugate (or adjoint) of an operator is the oper-ator Q* such that(SIÔ8) = (Ô* Slg) (for all f and g).[3.20](A hermitian operator, then, is equal to its hermitian conjugate: Q = Q*.)(a) Find the hermitian conjugates of x, i, and d/dx.(b) Construct the hermitian conjugate of the harmonic oscillator raising operator,a4 (Equation 2.47).(c) Show that (QR)* = R* ô*.1(mwx)'|.(2.47)+2m

(a) We know the position operator is a Hermitian operator, and the hermitian conjugate of a…

Problem 3.5 The hermitian conjugate (or adjoint) of an operator Ô is the oper- ator Q* such that (SIê8) = (Ô' ƒlg) (for all f and g). [3.20] (A hermitian operator, then, is equal to its hermitian conjugate: Ô = ê*.) (a) Find the hermitian conjugates of x, i, and d/dx. (b) Construct the hermitian conjugate of the harmonic oscillator raising operator, a4 (Equation 2.47). (c) Show that (QR)* = R* Ô*.

Problem 3.5 The hermitian conjugate (or adjoint) of an operator Ô is the oper- ator Q* such that (SIê8) = (Ô' ƒlg) (for all f and g). [3.20] (A hermitian operator, then, is equal to its hermitian conjugate: Ô = ê.) (a) Find the hermitian conjugates of x, i, and d/dx. (b) Construct the hermitian conjugate of the harmonic oscillator raising operator, a4 (Equation 2.47). (c) Show that (QR) = R* Ô*.