Since the early part of the twentieth century, the use of integral equations has developed into a range of tools for the study of partial differential equations. This includes the use of single- and double-layer potentials to treat classical boundary value problems. The aim of t…
We consider the time-dependent Schrödinger equation on a Riemannian manifold A with a potential that localizes a certain subspace of states close to a fixed submanifold C. When we scale the potential in the directions normal to C by a parameter [epsilon]<<1, the solutions concen…
We consider the time-dependent Schrödinger equation on a Riemannian manifold A with a potential that localizes a certain subspace of states close to a fixed submanifold C. When we scale the potential in the directions normal to C by a parameter [epsilon]<<1, the solutions concen…