Effective Hamiltonians for Constrained Quantum Systems - Couverture souple

Wachsmuth, Jakob; Teufel, Stefan

Couverture souple

ISBN 10 : 0821894897 ISBN 13 : 9780821894897

Editeur : American Mathematical Society, 2014

Synopsis

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.

A propos du livre

À propos de l?auteur

Jakob Wachsmuth, University of Bremen, Germany.

Stefan Teufel, University of Tubingen, Germany.

Détails de l'édition

• Éditeur: American Mathematical Society
• Date d'édition: 2014
• Langue: anglais
• ISBN 10: 0821894897
• ISBN 13: 9780821894897
• Reliure: Broché
• Nombre de pages: 83
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible