Contents -- Chapter 1. Introduction -- 1.1. The model -- 1.2. Comparison with existing results -- Chapter 2. Main results -- 2.1. Effective dynamics on the constraint manifold -- 2.2. The effective Hamiltonian -- 2.3. Approximation of eigenvalues -- 2.4. Application to quantum wave guides -- Chapter 3. Proof of the main results -- 3.1. Proof of adiabatic decoupling -- 3.2. Pullback of the results to the ambient space -- 3.3. Derivation of the effective Hamiltonian -- 3.4. Proof of the approximation of eigenvalues -- Chapter 4. The whole story
4.1. Elliptic estimates for the Sasaki metric4.2. Expansion of the Hamiltonian -- 4.3. Construction of the superadiabatic subspace -- Appendix A. Geometric definitions and conventions -- A.1. Manifolds of bounded geometry -- A.2. The geometry of submanifolds -- Bibliography
