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The Casimir effect of an ideal Bose gas trapped in a generic power-lawpotential and confined between two slabs with Dirichlet, Neumann, and periodicboundary conditions is investigated systematically, based on the grandpotential of the ideal Bose gas, the Casimir potential and force arecalculated. The scaling function is obtained and discussed. The special casesof free and harmonic potentials are also discussed. It is found that when T<Tc(where Tc is the critical temperature of Bose-Einstein condensation), theCasimir force is a power-law decay function; when T>Tc, the Casimir force is anexponential decay function; and when T>>Tc, the Casimir force vanishes.

Casimir effect of an ideal Bose gas trapped in a generic power-law potential