Inverse and Algebraic Quantum Scattering Theory: Proceedings of a Conference Held at Lake Balaton, Hungary, 3–7 September 1996

Anne Boutet de Monvel (auth.), Barnabás Apagyi, Gábor Endrédi, Péter Lévay (eds.)354063021X, 9783540630210

This volume contains three interrelated, beautiful, and useful topics of quantum scattering theory: inverse scattering theory, algebraic scattering theory and supersymmetrical quantum mechanics. The contributions cover such issues as coupled-channel inversions at fixed energy, inversion of pion-nucleon scattering cross-sections into potentials, inversions in neutron and x-ray reflection, 3-dimensional fixed-energy inversion, inversion of electron scattering data affected by dipole polarization, nucleon-nucleon potentials by inversion versus meson-exchange theory, potential reversal and reflectionless impurities in periodic structures, quantum design in spectral, scattering, and decay control, solution hierarchy of Toda lattices, etc.

---

Table of contents :
Front Matter….Pages I-XV
New Inverse Spectral Problem and Its Application….Pages 1-12
Inverse Problem on the Entire Line and Some Connected Questions of Spectral Theory….Pages 13-29
Qualitative Physics in Spectral, Scattering and Decay Control….Pages 30-44
Ambiguities in Inversion Potentials for Light Nuclear Ion Scattering….Pages 45-53
Coupled-Channel Marchenko Inversion in One Dimension with Thresholds….Pages 54-63
One-Dimensional Inversion in Neutron and X-Ray Reflection….Pages 64-74
Non-standard Information in Optical Model Analyses….Pages 75-87
Numerical Method for Solving the Inverse Problem of Quantum Scattering Theory….Pages 88-97
The Inverse Scattering Problem for Coupled Channels with the Modified Newton-Sabatier Method….Pages 98-111
Energy-Dependent Potentials Obtained by IP Inversion….Pages 112-123
Modeling of Nucleon-Nucleon Potentials, Quantum Inversion versus Meson Exchange Pictures….Pages 124-140
Inversion Potentials for Meson-Nucleon and Meson-Meson Interactions….Pages 141-155
Fixed-Energy Inversion of Polarisation-Corrected Electron-Atom Scattering Phase-Shifts into Effective Potentials….Pages 156-168
Pion Nucleus Interaction from Inverse Scattering Theory and a Test of Charge Symmetry….Pages 169-176
NN Potentials with Explicit Momentum Dependence Obtained from Generalized Darboux Transformations….Pages 177-186
Unitarity and the Scattering Phase Shifts for Inversion Studies….Pages 187-196
Potential Reversal and Reflectionless Impurities in Periodic Structures….Pages 197-203
The Method of the Weakly Conjugate Operator….Pages 204-226
Solutions to the Hierarchy of the Periodic Toda Lattices….Pages 227-236
Spectrum Generating Algebras and Dynamic Symmetries in Scattering….Pages 237-254
Algebraic Coupled-Channels Formalism for Heavy Ions near the Coulomb Barrier….Pages 255-272
Algebraic Scattering Theory and Light Heavy-Ion Reactions….Pages 273-286
Geometrical Relation of the SACM….Pages 287-294
Phase-Equivalent Complex Potentials….Pages 295-313
Exactly Solvable Models for Two-Dimensional Quantum Systems….Pages 314-341
Exactly Solvable Quantum Models for Investigation of Nonadiabatic Transitions….Pages 342-353
Modified Symmetry Generators for SO (3, 2) and Algebraic Scattering Theory….Pages 354-362
Analytical Results on Generating Phase-Equivalent Potentials by Supersymmetry: Removal and Addition of Bound States….Pages 363-372
Multidimensional Inverse Scattering with Fixed-Energy Data….Pages 373-384
Back Matter….Pages 385-388