Fundamentals of scattering theory and resonances in quantum mechanics
-
Peter D. Hislop
hislop@ms.uky.edu
Downloads
DOI:
https://doi.org/10.4067/S0719-06462012000300001Abstract
We present the basics of two-body quantum-mechanical scattering theory and the theory of quantum resonances. The wave operators and S-matrix are constructed for smooth, compactly-supported potential perturbations of the Laplacian. The meromorphic continuation of the cut-off resolvent is proved for the same family of Schrödinger operators. Quantum resonances are defined as the poles of the meromorphic continuation of the cut-off resolvent. These are shown to be the same as the poles of the meromorphically continued S-matrix. The basic problems of the existence of resonances and estimates on the resonance counting function are described and recent results are presented.
Keywords
Similar Articles
- Stephen McDowall, Optical Tomography for Media with Variable Index of Refraction , CUBO, A Mathematical Journal: Vol. 11 No. 5 (2009): CUBO, A Mathematical Journal
- Meriem Djibaoui, Toufik Moussaoui, Variational methods to second-order Dirichlet boundary value problems with impulses on the half-line , CUBO, A Mathematical Journal: Vol. 24 No. 2 (2022)
- Jürgen Tolksdorf, Dirac Type Gauge Theories – Motivations and Perspectives , CUBO, A Mathematical Journal: Vol. 11 No. 1 (2009): CUBO, A Mathematical Journal
- M.O Korpusov, A. G. Sveschnikov, On blowing-up of solutions of Sobolev-type equation with source , CUBO, A Mathematical Journal: Vol. 7 No. 1 (2005): CUBO, A Mathematical Journal
- T. A. Burton, Bo Zhang, Bounded and periodic solutions of integral equations , CUBO, A Mathematical Journal: Vol. 14 No. 1 (2012): CUBO, A Mathematical Journal
- Shigeki Matsutani, Relations of al Functions over Subvarieties in a Hyperelliptic Jacobian , CUBO, A Mathematical Journal: Vol. 7 No. 3 (2005): CUBO, A Mathematical Journal
- V´Ä±ctor Ayala, Marcos M. Diniz, Jos´e C.P. Lima, Jos´e M.M. Veloso, Ivan Tribuzy, Wave Front Sets Singularities of Homogeneous Sub-Riemannian Three Dimensional Manifolds , CUBO, A Mathematical Journal: Vol. 10 No. 2 (2008): CUBO, A Mathematical Journal
- Syed Abbas, Weighted pseudo almost automorphic solutions of fractional functional differential equations , CUBO, A Mathematical Journal: Vol. 16 No. 1 (2014): CUBO, A Mathematical Journal
- Junwei Liu, Chuanyi Zhang, Existence and stability of almost periodic solutions to impulsive stochastic differential equations , CUBO, A Mathematical Journal: Vol. 15 No. 1 (2013): CUBO, A Mathematical Journal
- Vikram Singh, Dwijendra N Pandey, Weighted pseudo Almost periodic solutions for fractional order stochastic impulsive differential equations , CUBO, A Mathematical Journal: Vol. 19 No. 1 (2017): CUBO, A Mathematical Journal
<< < 1 2 3 4 5 6 7 8 9 10 11 12 > >>
You may also start an advanced similarity search for this article.
