Physics – Quantum Physics
Scientific paper
2000-01-18
Physics
Quantum Physics
27 pages with 1 figure, submitted to Phys. Rev. A
Scientific paper
10.1103/PhysRevA.63.042112
We derive an effective Hamiltonian for a quantum system constrained to a submanifold (the constraint manifold) of configuration space (the ambient space) by an infinite restoring force. We pay special attention to how this Hamiltonian depends on quantities which are external to the constraint manifold, such as the external curvature of the constraint manifold, the (Riemannian) curvature of the ambient space, and the constraining potential. In particular, we find the remarkable fact that the twisting of the constraining potential appears as a gauge potential in the constrained Hamiltonian. This gauge potential is an example of geometric phase, closely related to that originally discussed by Berry. The constrained Hamiltonian also contains an effective potential depending on the external curvature of the constraint manifold, the curvature of the ambient space, and the twisting of the constraining potential. The general nature of our analysis allows applications to a wide variety of problems, such as rigid molecules, the evolution of molecular systems along reaction paths, and quantum strip waveguides.
No associations
LandOfFree
Geometric Phase, Curvature, and Extrapotentials in Constrained Quantum Systems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Geometric Phase, Curvature, and Extrapotentials in Constrained Quantum Systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Geometric Phase, Curvature, and Extrapotentials in Constrained Quantum Systems will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-429799