Ebook: Resonances The Unifying Route Towards the Formulation of Dynamical Processes Foundations and Applications in Nuclear, Atomic and Molecular Physics: Proceedings of a Symposium Held at Lertorpet, Värmland, Sweden, August 19–26, 1987

Scattering theory is of interest to physicists and to chemists and has a wide variety of applications, but it also presents a considerable challenge to mathematicians, including numerical analysts. Within the Schr?dinger picture in this volume are collected the various theoretical and mathematical treatments of scattering together with a host of reviews of its applications to atomic and nuclear physics, to surface physics and chemistry, for example trapping of atoms on surfaces, and to amorphous condensed systems. The reviews give a concise and pedagogically useful presentation of the state of the art, and may serve as introductions for newcomers, in particular for graduate students.

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Scattering theory is of interest to physicists and to chemists and has a wide variety of applications, but it also presents a considerable challenge to mathematicians, including numerical analysts. Within the Schr?dinger picture in this volume are collected the various theoretical and mathematical treatments of scattering together with a host of reviews of its applications to atomic and nuclear physics, to surface physics and chemistry, for example trapping of atoms on surfaces, and to amorphous condensed systems. The reviews give a concise and pedagogically useful presentation of the state of the art, and may serve as introductions for newcomers, in particular for graduate students.
Content:
Front Matter....Pages -
Introduction to Rigged Hilbert Spaces (RHS)....Pages 1-10
Comparison between different notions of resonances....Pages 11-19
Resonances and semiclassical analysis....Pages 21-33
Resonances with a background potential....Pages 35-46
On the general inversion problem....Pages 47-55
Weyl's theory studies and the one-dimensional almost periodic Schr?dinger equation....Pages 57-75
A generalization of Rouch?'s theorem with application to resonances....Pages 77-85
Generalization of M?ller's variational principle....Pages 87-103
Resonance state expansions in nuclear physics....Pages 105-117
Mittag-Leffler expansions in nuclear physics....Pages 119-127
On the analytical continuation of the partial wave S-matrix using complex scaling techniques....Pages 129-151
Calculation of resonant wave functions in nuclear physics....Pages 153-177
The use of Gamow functions in nuclear problems....Pages 179-200
Resonances as an Eigenvalue problem....Pages 201-214
A model for studying time dependent quantum mechanical processes and its application for quasi-stationary states....Pages 215-232
Time-dependent dynamics applied to electron transfer....Pages 233-252
Semiclassical description of resonances....Pages 253-280
Regge poles and atom-molecule diffraction....Pages 281-311
Energy shifts and widths in atomic and molecular physics: Multichannel approach....Pages 313-327
Two study cases in the calculation of resonances using the multichannel Schr?dinger equation....Pages 329-344
Multichannel complex scaled Titchmarsh Weyl theory a model for diatomic fragmentation....Pages 345-382
On the way to a multiconfiguration treatment of resonance phenomena in atoms....Pages 383-431
Resonant states in the microscopic cluster model....Pages 433-453
A note on the cluster model and complex scaling....Pages 455-457
Complex scaling applied to trapping of atoms and molecules on solid surfaces....Pages 459-474
On a theorem for complex symmetric matrices and its relevance in the study of decay phenomena....Pages 475-483
Creation of long range order in amorphous condensed systems....Pages 485-540
The lertorpet symposium view on a generalized inner product....Pages 541-552
Back Matter....Pages -

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Scattering theory is of interest to physicists and to chemists and has a wide variety of applications, but it also presents a considerable challenge to mathematicians, including numerical analysts. Within the Schr?dinger picture in this volume are collected the various theoretical and mathematical treatments of scattering together with a host of reviews of its applications to atomic and nuclear physics, to surface physics and chemistry, for example trapping of atoms on surfaces, and to amorphous condensed systems. The reviews give a concise and pedagogically useful presentation of the state of the art, and may serve as introductions for newcomers, in particular for graduate students.
Content:
Front Matter....Pages -
Introduction to Rigged Hilbert Spaces (RHS)....Pages 1-10
Comparison between different notions of resonances....Pages 11-19
Resonances and semiclassical analysis....Pages 21-33
Resonances with a background potential....Pages 35-46
On the general inversion problem....Pages 47-55
Weyl's theory studies and the one-dimensional almost periodic Schr?dinger equation....Pages 57-75
A generalization of Rouch?'s theorem with application to resonances....Pages 77-85
Generalization of M?ller's variational principle....Pages 87-103
Resonance state expansions in nuclear physics....Pages 105-117
Mittag-Leffler expansions in nuclear physics....Pages 119-127
On the analytical continuation of the partial wave S-matrix using complex scaling techniques....Pages 129-151
Calculation of resonant wave functions in nuclear physics....Pages 153-177
The use of Gamow functions in nuclear problems....Pages 179-200
Resonances as an Eigenvalue problem....Pages 201-214
A model for studying time dependent quantum mechanical processes and its application for quasi-stationary states....Pages 215-232
Time-dependent dynamics applied to electron transfer....Pages 233-252
Semiclassical description of resonances....Pages 253-280
Regge poles and atom-molecule diffraction....Pages 281-311
Energy shifts and widths in atomic and molecular physics: Multichannel approach....Pages 313-327
Two study cases in the calculation of resonances using the multichannel Schr?dinger equation....Pages 329-344
Multichannel complex scaled Titchmarsh Weyl theory a model for diatomic fragmentation....Pages 345-382
On the way to a multiconfiguration treatment of resonance phenomena in atoms....Pages 383-431
Resonant states in the microscopic cluster model....Pages 433-453
A note on the cluster model and complex scaling....Pages 455-457
Complex scaling applied to trapping of atoms and molecules on solid surfaces....Pages 459-474
On a theorem for complex symmetric matrices and its relevance in the study of decay phenomena....Pages 475-483
Creation of long range order in amorphous condensed systems....Pages 485-540
The lertorpet symposium view on a generalized inner product....Pages 541-552
Back Matter....Pages -
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