Inverse and Algebraic Quantum Scattering Theory: Proceedings of a Conference Held at Lake Balaton, Hungary, 3-7 September 1996 (Lecture Notes in Physics)

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. 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 This volume contains three interrelated topics of quantum scattering theory: inverse scattering theory; algebraic scattering theory; and supersymmetrical quantum mechanics. Topics covered include 3-dimensional fixed-energy inversion and solution hierarchy of Toda lattices.