Bose-Einstein condensation and the Casimir effect for an ideal Bose gas confined between two slabs

We study the Casimir effect for a 3D system of ideal Bose gas in a slab geometry with a Dirichlet boundary condition. We calculate the temperature (T) dependence of the Casimir force below and above the Bose-Einstein condensation temperature (Tc). At T ≤ Tc the Casimir force vanishes as [T/Tc]3/2. For T ∼> Tc it weakly depends on temperature. For T >> Tc it vanishes exponentially. At finite temperatures this force for thermalized photons in between two plates has a classical expression which is independent of ℎ. At finite temperatures the Casimir force for our system depends on ℎ