In the limit ℏ→0, we analyze a class of Schr\"odinger operators H_ℏ = ℏ² L + ℏ W + V id_Eh acting on sections of a vector bundle Eh over a Riemannian manifold M where L is a Laplace type operator, W is an endomorphism field and the potential energy V has a non-degenerate minimum at some point p ∈ M. We construct quasimodes of WKB-type near p for eigenfunctions associated with the low lying eigenvalues of H_ℏ. These are obtained from eigenfunctions of the associated harmonic oscillator H_p,ℏ at p, acting on C^∞(T_pM, Eh_p).