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!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Hermitian calculation question

**Physics Forums | Science Articles, Homework Help, Discussion**