# Homework Help: P wave superconductivity

Tags:
1. Feb 3, 2017

### DeathbyGreen

Hello! So I'm really stuck in a personal quest to derive Kitaev's 1D p wave superconductivity model, and I'm stuck on the seemingly simplest part.

1. The problem statement, all variables and given/known data

In the Bogluibov transformation, we get two coefficients from the equations

$|v_{k}|^{2}+ |u_{k}|^{2}= 1$

$v_{k}=(\frac{E_{Bulk}-\epsilon_{k}}{\Delta_{k}})\mu_{k}$

Where $E_{Bulk} = \sqrt{\epsilon_{k}^{2} + |\Delta_{k}|^{2}}$

3. The attempt at a solution

I cannot derive the correct expression for $u_{k}$

$u_{k} = \frac{\Delta_{k}}{|\Delta_{k}|}\frac{\sqrt{E_{Bulk}+\epsilon_{k}}}{\sqrt{2E_{Bulk}}}$

I know it's just simple algebra, but I've been working on it for hours without any progress and I can't find any sources online that show the derivation :O