Reading back in my book, Greiner's "QM :an introduction" I found a formula I don't understand.(adsbygoogle = window.adsbygoogle || []).push({});

Let [tex]\alpha[/tex] be a real number, [tex]\Delta \hat{A}, \Delta \hat{B}[/tex] be Hermitian operators. Now I have

[tex]\int (\alpha \Delta \hat{A} - i \Delta \hat{B})^* \psi^* (\alpha \Delta \hat{A} - i \Delta \hat{B}) \psi dx

= \int \psi^* (\alpha \Delta \hat{A} + i \Delta \hat{B}) ( \alpha \Delta \hat{A} - i \Delta \hat{B}) \psi dx[/tex]

This leads to an expected result to prove Heisenberg's Uncertainty Relations, but I think the right-hand side of this formula should be

[tex]\int \psi^* (\alpha \Delta \hat{A}^* + i \Delta \hat{B}^*) (\alpha \Delta \hat{A} - i \Delta \hat{B}) \psi dx[/tex]

I should be wrong, but I don't know why. Operators [tex]\Delta \hat{A}, \Delta \hat{B}[/tex] can be complex... (or are they always real?) So will anyone tell me how or why it's correct?

Thanks in advance!

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# Homework Help: Hermitian calculation question

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