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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

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