Effective Hamiltonians for Constrained Quantum Systems - Memoirs of the American Mathematical Society (Paperback)
  • Effective Hamiltonians for Constrained Quantum Systems - Memoirs of the American Mathematical Society (Paperback)
zoom

Effective Hamiltonians for Constrained Quantum Systems - Memoirs of the American Mathematical Society (Paperback)

(author), (author)
£67.95
Paperback 83 Pages / Published: 30/06/2014
  • We can order this

Usually dispatched within 2 weeks

  • This item has been added to your basket
The authors consider the time-dependent Schroedinger 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 Schroedinger 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.

Publisher: American Mathematical Society
ISBN: 9780821894897
Number of pages: 83
Dimensions: 254 x 178 mm

You may also be interested in...

The Physics of Quantum Mechanics
Added to basket
Group Theory
Added to basket
£62.99
Hardback
Mathematics for Physicists
Added to basket
Mrs. Perkins's Electric Quilt
Added to basket
Computational Physics
Added to basket
The Language of Physics
Added to basket
An Introduction to Quantitative Finance
Added to basket
The Mathematical Mechanic
Added to basket
Inside Interesting Integrals
Added to basket
Measurements and their Uncertainties
Added to basket
Effective Computation in Physics
Added to basket

Please sign in to write a review

Your review has been submitted successfully.