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**1. Homework Statement**

Show any operator Q that commutes with the Hamiltonian, [Q,H] = 0, is conserved in the above sense (d/dt〈Ψ|QΨ〉 = 0).

The solution to this problem is as follows:

iħd/dt〈Ψ|QΨ〉 = (iħd/dt〈Ψ|)|QΨ〉 + 〈Ψ|(|Qiħd/dtΨ〉 = –〈HΨ|QΨ〉 + 〈Ψ|QHΨ〉 = 〈Ψ|[QH]Ψ〉 = 0.

What I am confused about is the second step:

[tex]

\[i\hbar \frac{d}{{dt}}\left\langle \psi \right|\left. {Q\psi } \right\rangle = \left\langle {i\hbar \frac{d}{{dt}}\psi } \right|\left. {Q\psi } \right\rangle + \left\langle \psi \right|\left. {Qi\hbar \frac{d}{{dt}}\psi } \right\rangle\]

[/tex]

Why is this true? Where did the sum come from? Why is the Hamiltonian before Q in the second term of the sum? What allows you to put it in that order? Does it matter (I assume it does since we're trying to prove a commutation relation here..)