  We study the spectrum of Schr\"odinger operators with matrix valued
potentials utilizing tools from infinite dimensional symplectic geometry. Using
the spaces of abstract boundary values, we derive relations between the Morse
and Maslov indices for a family of operators on a Hilbert space obtained by
perturbing a given self-adjoint operator by a smooth family of bounded
self-adjoint operators. The abstract results are applied to the Schr\"{o}dinger
operators with quasi-periodic, Dirichlet and Neumann boundary conditions. In
particular, we derive an analogue of the Morse-Smale Index Theorem for the
multidimensional Schr\"odinger operators with periodic potentials. For quasi
convex domains in $\mathbb{R}^n$ we recast the results connecting the Morse and
Maslov indices using the Dirichlet and Neumann traces on the boundary of the
domain.
