| Vorderseite | [latex]State the effective range expansion of $ k^{2l+1} \cot(\delta_l (k)) $.[/latex] |
| Rückseite | [latex]$ k^{2l+1} \cot(\delta_l (k)) = -\frac{1}{a_l} + \frac{r_l}{2} k^2 + ... $[/latex] |
| Tags | AQM3 |
| Vorderseite | [latex]The field operators which annihilate and create a particle at position $ \vec{x} $ are $ \Psi (\vec{x}) $ and $ \Psi^+ (\vec{x}) $, respectively. Write down the particle number density at position $ \vec{x} $ in terms of the field operators.[/latex] |
| Rückseite | [latex]$ n(\vec{x}) = \Psi^+(\vec{x}) \Psi(\vec{x}) $[/latex] |
| Tags | AQM13 |
| Vorderseite | [latex]Assuming $ a > 0 $, give the result of the Gaussian integral $ \int_{-\infty}^{\infty} dx e^{-ax^2} $. [/latex] |
| Rückseite | [latex]$ \int_{-\infty}^{\infty} dx e^{-ax^2} = \sqrt{ \frac{\pi}{a} } $[/latex] |
| Tags | AQM5 |