# Transforming BCS state to real space

## Main Question or Discussion Point

What is the most straightforward way of transforming a BCS type state, $\left| \Phi \right\rangle = \prod(u_k + v_k F^{\dagger}_{k} F^{\dagger}_{-k}) \left| vac \right\rangle$, to real space?

Would it be valid to transform states of the form

$F^{\dagger}_k F^{\dagger}_{-k} \longrightarrow a^{\dagger}_{n} a^{\dagger}_{m},~~~~F^{\dagger}_{k_1} F^{\dagger}_{-k_1} F^{\dagger}_{k_2} F^{\dagger}_{-k_2} \longrightarrow a^{\dagger}_{n} a^{\dagger}_{m} a^{\dagger}_{p} a^{\dagger}_{q}, ~~$ etc.,

separately using multidimensional discrete FT? Is there an easier/more efficient way? Thanks for your help!