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The authors consider the time-dependent Schrodinger equation on a Riemannian manifold $mathcal$ with a potential that localizes a certain subspace of states close to a fixed submanifold $mathcal$. When the authors scale the potential in the directions normal to $mathcal$ by a parameter $varepsilonll 1$ the solutions concentrate in an $varepsilon$-neighborhood of $mathcal$. This situation occurs for example in quantum wave guides and for the motion of nuclei in electronic potential surfaces in quantum molecular dynamics. The authors derive an effective Schrodinger equation on the...

Microlocal analysis is a field of mathematics that was invented in the mid-20th century for the detailed investigation of problems from partial differential equations, which incorporated and made rigorous many ideas that originated in physics. Since then it has grown to a powerful machine which is used in global analysis, spectral theory, mathematical physics and other fields, and its further development is a lively area of current mathematical research. In this book extended abstracts of the conference 'Microlocal Methods in Mathematical Physics and Global Analysis', which was held at the...