# How to write a wave-fuction of bose einstein condesate bosons in second quantization representation?

Can we write wave function of bose einstein condensation like this $$|\psi \rangle=\frac{{c^{\dagger}}^N}{ \sqrt{N!}} |0\rangle$$. Or it will be different?

$$|\mathrm{BEC}\rangle = \frac{1}{\sqrt{N!}}(a^\dagger_0)^N\,|0\rangle,$$ where $$a^\dagger_0$$ is the (bosonic) creation operator for the $$\mathbf{k} = 0$$ state.