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Autor:
Kalyan B. Sinha, W O Amrein
Publikováno v:
Journal of Physics A: Mathematical and General. 39:9231-9254
We present stationary expressions for the on-shell time delay operator and for its trace in quantum-mechanical potential scattering. The trace of this operator is shown to represent the time delay for a monoenergetic and well-collimated beam of initi
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::d9fd49995d3cda6987d3bd5b15f3f20a
https://doi.org/10.1088/0305-4470/39/29/016
https://doi.org/10.1088/0305-4470/39/29/016
The conjugate operator method is a powerful recently developed technique for studying spectral properties of self-adjoint operators. One of the purposes of this volume is to present a refinement of the original method due to Mourre leading to essenti
Publikováno v:
Annales Henri Poincaré. 3:1215-1232
We consider anisotropic Schrodinger operators $ H = -{\Delta} + V $ in $ L^{2}(\mathbb{R}^n) $ . To certain asymptotic regions F we assign asymptotic Hamiltonians H F such that (a) $ \sigma(H_F) \subset \sigma_{\textrm{ess}}(H) $ , (b) states with en
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::9f40e88ef80f38a5a2d1c384c4307984
https://doi.org/10.1007/s000230200003
https://doi.org/10.1007/s000230200003
Autor:
D. B. Pearson, W. O. Amrein
Publikováno v:
Mathematical Physics, Analysis and Geometry. 1:193-221
This paper presents a new approach to spectral theory for theSchrodinger Operator on the half-line. Solutions of nonlinearRiccati-type equations related to the Schrodinger equation at realspectral parameter λ are characterised by means of their clus
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::e3318ae516fad819894ecfc7372e0c47
https://doi.org/10.1023/a:1009759202730
https://doi.org/10.1023/a:1009759202730
Autor:
W O Amrein, D B Pearson
Publikováno v:
Journal of Physics A: Mathematical and General. 30:5361-5379
We prove that the probability of finding a scattered quantum-mechanical particle at large times in a truncated cone is identical with the scattered flux, integrated over time, across a distant spherical surface subtending this cone. The theory applie
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::db10ef345e6c58ec6b40d8932f4a30ec
https://doi.org/10.1088/0305-4470/30/15/022
https://doi.org/10.1088/0305-4470/30/15/022
Autor:
Kalyan B. Sinha, W O Amrein
Publikováno v:
Linear Algebra and its Applications. :425-435
We give an algebraic derivation of the canonical form of a generic pair of projections. The result is used to determine the spectral shift of a pair of projections and various properties of Fredholm pairs.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d39cce8aab2f062f4dd7ca793872cac4
https://doi.org/10.1016/0024-3795(94)90454-5
https://doi.org/10.1016/0024-3795(94)90454-5
Autor:
W. O. Amrein, Philippe Jacquet
Publikováno v:
Physical Review. A, Vol. 75, No 022106 (2007)
This paper concerns time-dependent scattering theory and in particular the concept of time delay for a class of one-dimensional anisotropic quantum systems. These systems are described by a Schr\"{o}dinger Hamiltonian $H = -\Delta + V$ with a potenti
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6cb974689ab3070e547682caffa1b6a0
https://doi.org/10.1103/physreva.75.022106
https://doi.org/10.1103/physreva.75.022106
Publikováno v:
Sturm-Liouville Theory
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::e1f6dfd8b54272a4d2419c8f428f21bc
https://doi.org/10.1007/3-7643-7359-8
https://doi.org/10.1007/3-7643-7359-8
Publikováno v:
C0-Groups, Commutator Methods and Spectral Theory of N-Body Hamiltonians ISBN: 9783034807326
A representation W of ℝ n with values in the group of automorphisms (i.e. linear multiplicative bijections) of a Banach algebra B has many interesting features due to the richness of the algebraic structure which comes into play. We have no intenti
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::fd97814186c392cbba7136f2d7711d34
https://doi.org/10.1007/978-3-0348-0733-3_5
https://doi.org/10.1007/978-3-0348-0733-3_5