Transforming BCS state to real space

auctor

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

Would it be valid to transform states of the form

[itex] 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}, ~~[/itex] etc.,

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

DrDu

There is a simple expression for a wavefunction with fixed number of particles. This wavefunction (see, e.g. the book by Schrieffer, Superconductivity) can be expressed in terms of two particle wavefunctions in direct space. See also p52:
http://www.google.de/url?sa=t&rct=j&...1EEmJg&cad=rja

auctor

Thank you, I think this should work.