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
- K. Kalyani, N. Seshagiri Rao, Coincidence point results of nonlinear contractive mappings in partially ordered metric spaces , CUBO, A Mathematical Journal: Vol. 23 No. 2 (2021)
- Bashir Ahmad, Amjad F. Albideewi, Sotiris K. Ntouyas, Ahmed Alsaedi, Existence results for a multipoint boundary value problem of nonlinear sequential Hadamard fractional differential equations , CUBO, A Mathematical Journal: Vol. 23 No. 2 (2021)
- M. Haviar, S. Kurtulík, A new class of graceful graphs: \(k\)-enriched fan graphs and their characterisations , CUBO, A Mathematical Journal: Vol. 23 No. 2 (2021)
- U. Traoré, Entropy solution for a nonlinear parabolic problem with homogeneous Neumann boundary condition involving variable exponents , CUBO, A Mathematical Journal: Vol. 23 No. 3 (2021)
- Saleh S. Almuthaybiri, Jagan Mohan Jonnalagadda, Christopher C. Tisdell, Existence and uniqueness of solutions to discrete, third-order three-point boundary value problems , CUBO, A Mathematical Journal: Vol. 23 No. 3 (2021)
- Masaya Kawamura, On an \(a\) \(priori\) \(L^\infty\) estimate for a class of Monge-Ampère type equations on compact almost Hermitian manifolds , CUBO, A Mathematical Journal: Vol. 24 No. 2 (2022)
- Fouad Fredj, Hadda Hammouche, On existence results for hybrid \(\psi-\)Caputo multi-fractional differential equations with hybrid conditions , CUBO, A Mathematical Journal: Vol. 24 No. 2 (2022)
- Andrew Craig, Miroslav Haviar, José São João, Dual digraphs of finite semidistributive lattices , CUBO, A Mathematical Journal: Vol. 24 No. 3 (2022)
- René Erlín Castillo, Babar Sultan, A derivative-type operator and its application to the solvability of a nonlinear three point boundary value problem , CUBO, A Mathematical Journal: Vol. 24 No. 3 (2022)
- Gradimir V. Milovanović, Abdullah Mir, Adil Hussain, Estimates for the polar derivative of a constrained polynomial on a disk , CUBO, A Mathematical Journal: Vol. 24 No. 3 (2022)
<< < 22 23 24 25 26 27 28 29 30 > >>
You may also start an advanced similarity search for this article.
