# Bose Einstein Condensation in Grand canonical ensemble

Why we develop formalism of Bose Einstein Condensation in framework of grand canonical ensemble ?

The only complication with the occupation number representation is what happens when we try to impose a constraint on the total number of particles. If I have ten particles and I know that the occupation number of state $$A$$ is 1, then I know that the occupation number of state $$B$$ cannot be 10, but if state $$A$$ is unoccupied then all the particles can be in state $$B$$. In other words the constraint means that different occupation numbers are not independent of each other, since they must sum to a fixed total. In the extreme case where I have only one particle, then as soon as I know that some state has an occupation number of 1, I immediately know all the other occupation numbers. This correlation between occupation numbers makes calculation much more complicated.