Effective Hamiltonians for constrained quantum systems
Author(s)
Bibliographic Information
Effective Hamiltonians for constrained quantum systems
（Memoirs of the American Mathematical Society, no.1083）
American Mathematical Society, 2014, c2013
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Note
Includes bibliographical references (p. 81-83)
"Volume 230, number 1083 (fifth of 5 numbers), July 2014
Description and Table of Contents
Description
The authors 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 the authors scale the potential in the directions normal to C by a parameter e≪1, the solutions concentrate in an e -neighborhood of C. 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 Schrödinger equation on the submanifold C and show that its solutions, suitably lifted to A, approximate the solutions of the original equation on A up to errors of order e 3 |t| at time t. Furthermore, the authors prove that the eigenvalues of the corresponding effective Hamiltonian below a certain energy coincide up to errors of order e3 with those of the full Hamiltonian under reasonable conditions.
Table of Contents
Introduction
Main results
Proof of the main results
The whole story
Appendix A. Geometric definitions and conventions
Bibliography
by "Nielsen BookData"