1
$\begingroup$

In the Bogoliubov theory for the weakly interacting Bose gas, the Bogoliubov transformation from bosonic creation (annihilation) operators $\hat{a}_p^{(\dagger)}$ to the new set of creation (annihilation) operators $\hat{\alpha}_p^{(\dagger)}$ is defined via

$\hat{a}_p=u_p\hat{\alpha}_{p}-v_p\hat{\alpha}_{-p}^{\dagger}$ and $\hat{a}_{-p}^{\dagger}=u_p\hat{\alpha}_{-p}^{\dagger}-v_p\hat{\alpha}_{p}$.

I have looked various textbooks and lecture notes, and $u_p$ and $v_p$ are mostly assumed to be real. Why? Does this have some deeper meaning?

$\endgroup$
1
$\begingroup$

No deep meaning. The only requirement on $u_p$ and $v_p$ is their normalisation condition: $$ |u_p|^2 + |v_p|^2 = 1.$$ For simplicity, and as usual in quantum mechanics, you just them to be real numbers.

$\endgroup$
1
  • $\begingroup$ I think there should be a - sign instead of the + one $\endgroup$ – Milarepa Jan 3 at 23:18

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.