  In the limit $\hbar\to 0$, we analyze a class of Schr\"odinger operators
$H_\hbar = \hbar^2 L + \hbar W + V\cdot \mathrm{id}$ acting on sections of a
vector bundle $\mathcal{Eh}$ 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 $p\in M$. We construct
quasimodes of WKB-type near $p$ for eigenfunctions associated with the low
lying eigenvalues of $H_\hbar$. These are obtained from eigenfunctions of the
associated harmonic oscillator $H_{p, \hbar}$ at $p$, acting on smooth
functions on the tangent space.
