Angelescu N., Verbeure A., Zagrebnov V.A. Quantum n-Vector Anharmonic Crystal I: 1/n-Expansion (42K, latex) ABSTRACT. We consider the finite-volume quantum $n$-vector anharmonic crystal in the large $n$ limit and compute corrections to the corresponding Hartree-Fock system. In particular we prove the complete $1/n$-asymptotic series of the free energy, the Gibbs canonical state, and the distributions of the displacement and squared displacement fluctuation operators.