Problem 3.5 The hermitian conjugate (or adjoint) of an operator Q is the oper- ator *...

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Problem 3.5 The hermitian conjugate (or adjoint) of an operator Q is the oper- ator ô* such that (SIêg) = (Ôt flg) (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 (2.47) p + (mwx) 2m Problem 3.5 The hermitian conjugate (or adjoint) of an operator Q is the oper- ator ô* such that (SIêg) = (Ôt flg) (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 (2.47) p + (mwx) 2m