Effective Hamiltonians for constrained quantum systems /

Effective Hamiltonians for constrained quantum systems / Jakob Wachsmuth, Stefan Teufel.

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Bibliographic Details
Online Access: Full Text (via ProQuest)
Main Authors: Wachsmuth, Jakob, 1981- (Author), Teufel, Stefan, 1970- (Author)
Format: eBook
Language:English
Published: Providence, Rhode Island : American Mathematical Society, 2013.
Series:Memoirs of the American Mathematical Society ; Volume 230, no. 1083.
Subjects:
Hamiltonian operator.
Quantum theory.
Eigenvalues.
Mechanics.
Table of Contents:
  • 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.

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