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A numerical algorithm for explicitly computing the spectrum of theLaplace-Beltrami operator on Calabi-Yau threefolds is presented. The requisiteRicci-flat metrics are calculated using a method introduced in previous papers.To illustrate our algorithm, the eigenvalues and eigenfunctions of theLaplacian are computed numerically on two different quintic hypersurfaces, someZ_5 x Z_5 quotients of quintics, and the Calabi-Yau threefold with Z_3 x Z_3fundamental group of the heterotic standard model. The multiplicities of theeigenvalues are explained in detail in terms of the irreducible representationsof the finite isometry groups of the threefolds.

Eigenvalues and Eigenfunctions of the Scalar Laplace Operator on Calabi-Yau Manifolds