  We construct pairs of compact K\"ahler-Einstein manifolds
$(M_i,g_i,\omega_i)$ ($i=1,2)$ of complex dimension $n$ with the following
properties: The canonical line bundle $L_i=\bigwedge^n T^*M_i$ has Chern class
$[\omega_i/2\pi]$, and for each integer $k$ the tensor powers $L_1^{\otimes k}$
and $L_2^{\otimes k}$ are isospectral for the bundle Laplacian associated with
the canonical connection, while $M_1$ and $M_2$ -- and hence $T^*M_1$ and
$T^*M_2$ -- are not homeomorphic. In the context of geometric quantization, we
interpret these examples as magnetic fields which are quantum equivalent but
not classically equivalent. Moreover, we construct many examples of line
bundles $L$, pairs of potentials $Q_1$, $Q_2$ on the base manifold, and pairs
of connections $\nabla_1$, $\nabla_2$ on $L$ such that for each integer $k$ the
associated Schr\"odinger operators on $L^{\otimes k}$ are isospectral.
