  We construct the Hadamard Green's function by using the eigenfunction, which
are obtained by solving the wave equation for the massless conformal scalar
field on the S^n-1 of a n-dimensional closed, static universe. We also consider
the half space case with both the Dirichlet and the Neumann boundary
conditions. Solving of eigenfunction and eigenvalues of the corresponding field
equation is interesting since the Casimir energy could be calculated
analytically by various methods.
