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WORLD SCIENTIFIC eBooks

Rigorous results in quantum dynamics : Liblice, Czechoslovakia, 10-15 June 1990

J. Dittrich, Pavel Exner

Published Jan 1, 1991• 2 citations
Publisher

Abstract

"The proceedings of the conference is devoted mainly to the mathematically rigorous approaches to the problems of quantum mechanics. The spectral properties of Schrödinger operators, including those on regions with a boundary and their generalizations, scattering theory and resonances, time-dependent Hamiltonians and quantum chaos, problems of statistical physics like spin systems, and others are discussed."--Publisher's website

DOI
10.1142/1330#t=toc

Related papers

Mathematical results in quantum mechanics : international conference in Blossin (Germany), May 17-21, 1993

Michael Demuth

This work contains the proceedings of the International Conference on Mathematical Results in Quantum Mechanics held in Blossin, Germany, May 17-21, 1993. It aims to draw attention to the recent developments in quantum mechanics and related mathematical problems. The book features sections not only on traditional subjects such as Schroedinger and Dirac operators and generalized Schroedinger generators, but also on stochastic spectral analysis, many-body problems and statistical physics, chaos, and operator theory and its applications.

Birkhäuser-Verlag eBooks•Jan 1, 1994•0 citations

Mathematical results in quantum mechanics : QMath7 conference, Prague, June 22-26, 1998

J. Dittrich, Pavel Exner, Miloš Tater

I Plenary talks.- An adiabatic theorem without a gap condition.- Two-dimensional periodic Pauli operator. The effective masses at the lower edge of the spectrum.- Spectral problems in the theory of photonic crystals.- Optimal eigenvalues for some Laplacians and Schroedinger operators depending on curvature.- The spectral shift operator.- On the scattering operator for the Schroedinger equation with a time-dependent potential.- H_2-construction and some applications.- Scattering with time periodic potentials and cyclic states.- Some geometry related to decay properties of the resolvent of a class of symmetric operators.- On some asymptotic formulas in the strong localization regime of the theory of disordered systems.- Spectral measures and category.- Quantum dots. A survey of rigorous results.- II Session talks.- A simple model of concentrated nonlinearity.- Anomalous electron trapping by magnetic flux tubes and electric current vortices.- On the absolutely continuous energy distribution of a quantum mechanical system in a bounded domain.- Some aspects of generalized contact interaction in one-dimensional quantum mechanics.- Traces and trace norms for semigroup differences...- About a resolvent formula.- The determinant anomaly in low-dimensional quantum systems.- Linear Boltzmann equation as the weak coupling limit of the random Schroedinger equation.- Coexistence of different spectral types for almost periodic Schroedinger equations in dimension one.- Dynamical localization for random Schroedinger operators and an application to the almost Mathieu operator.- On fractal structure of the spectrum for periodic point perturbations of the Schroedinger operator with a uniform magnetic field.- A Weyl-Berry formula for the scattering operator associated to self-similar potentials on the line.- Localization and Lifshitz tails for random quantum waveguides.- Birman-Schwinger analysis for bound states in a pair of parallel quantum waveguides with a semitransparent boundary.- On the absolute continuity of spectra of periodic elliptic operators.- Hardy inequalities for magnetic Dirichlet forms.- Adiabatic curvature, chaos and the deformation of Riemann surfaces.- Operator interpretation of resonances arising in spectral problems for 2 x 2 matrix Hamiltonians.- On the operator-norm convergence of the Trotter-Kato product formula.- A particular case of the inverse problem for the Sturm-Liouville equation with parameter dependent potential.- One-dimensional Schroedinger operators with decaying potentials.- Stability of limiting absorption under singular perturbations.- Existence of averaging integrals for self-adjoint operators.- Monotonicity versus non-monotonicity in random operators.- A model in perturbation theory.- Band gap of the spectrum in periodically curved quantum waveguides.- A list of other talks.- A list of participants.

Birkhäuser-Verlag eBooks•Jan 1, 1999•0 citations

Order,Disorder and Chaos in Quantum Systems: Proceedings of a conference held at Dubna, USSR on October 17–21 1989

Pavel Exner, Neidhardt, Exner

1. Schroedinger operators : spectra, scattering and semiclassical behaviour.- Negative discrete spectrum of the Schroedinger operator with large coupling constant : qualitative discussion.- Discrete spectrum in the gaps of the continuous one in the large-coupling-constant limit.- On the asymptotics of discrete spectrum for the Schroedinger operator in electric and homogeneous magnetic fields.- Asymptotics of the discrete spectrum of Hamiltonians of quantum systems with a homogeneous magnetic field.- Asymptotics of eigenvalues for many-particle Hamiltonians at symmetry subspaces.- Spectral asymptotics with highly accurate remainder estimates.- Bound states and resonances in quantum wires.- Spectral properties of the operators H? = ??XX + p(x)? + v(?x), p is periodic.- Discrete spectrum for a periodic Schroedinger operator perturbed by a decreasing potential.- On a complete description of the principal discrete series of spectral invariants of the Hill operator.- WKB-approximations from the perturbation theory viewpoint.- Moving potentials and the completeness of wave operators. Part II : Propagating observables on scattering states.- Representation of the three-body S-matrix in terms of effective amplitudes.- A three-body one-dimensional system with increasing interaction : wave function asymptotics.- Surprises of quantum tunneling (something about the velocity of sub-barrier motion).- 2. Point and contact interactions, self-adjoint extensions.- Lifshitz tails and non-Lifshitz tails for one-dimensional random point interactions.- Point interactions with an internal structure as limits of nonlocal point interactions.- Green's function for the Aharonov-Bohm effect with a non-Abelian gauge group.- A model of zero-width slits and the real diffraction problem.- Construction of an inelastic scatterer in nanoelectronics by the extension-theory methods.- On boundary theory for Schroedinger operators and stochastic processes.- Dirac Hamiltonian with Coulomb potential and contact intraction on a sphere.- Self-adjoint extensions of Schroedinger operators with singular potentials.- Currents and the extension theory.- 3. Quantum chaos.- Chaotic quantum billiards.- Relevance of the localization to quasienergy statistics in quantum chaotic systems.- Singular continuous quasi-energy spectrum in the kicked rotator with separable perturbation : onset of quantum chaos ?.- Relation between correlation functions and spectrum statistics in the region of quantum chaos.- 4. Other topics.- Localization effects in non-homogeneous dielectrics.- A self-adjoint dilation of the linear Boltzmann operator.- Kato problem for functional-differential equations and difference Schroedinger operators.- An existence theorem for some nonlinear nonlocal Schroedinger operators and the solitonlike dynamics for the corresponding dynamical systems.- The Sturm-Liouville problem with a potential linear in spectral parameter.- Stochastic model of tree growth.- Critical phenomenon in the stationary model of random growth.- On a quantum-classical connection, hidden symmetries and a model of Josephson junction.- Open multiquantum systems. Method of a generating functional.- Generalized functions and their applications.- List of unpublished contributions.- List of participants.

•Jul 2, 1990•1 citation

Quantum field theory, statistical mechanics, and nonrelativistic quantum systems : a conference on spectral theory and mathematical physics in honor of Barry Simon's 60th birthday, March 27-31, 2006, California Institute of Technology, Pasadena, California

Fritz Gesztesy

Quantum field theory, statistical mechanics: Perspectives in statistical mechanics by M. Aizenman Coherent infrared representations in non-relativistic QED by T. Chen and J. Frohlich Quantum spin systems after DLS 1978 by B. Nachtergaele Barry Simon's contributions to quantum field theory by L. Rosen Nonrelativistic two-body and $N$-body quantum systems, resonances: Isoperimetric inequalities for eigenvalues of the Laplacian by M. S. Ashbaugh and R. D. Benguria Non-self-adjoint operators and pseudospectra by E. B. Davies Barry Simon's contribution to non-relativistic quantum mechanics: Two-body and $N$-body Schrodinger operators and resonances by R. Froese $N$-body quantum scattering and quantum resonances: An overview by C. Gerard Mathematical analysis of Born-Oppenheimer approximations by G. A. Hagedorn and A. Joye Perturbation theory and atomic resonances since Schrodinger's time by E. M. Harrell II On a theorem for quantum mechanical scattering theory by A. Lenard Analytic criteria in the qualitative spectral analysis of the Schrodinger operator by V. Maz'ya The spectral geometry of geometrically finite hyperbolic manifolds by P. Perry Topics in the theory of positive solutions of second-order elliptic and parabolic partial differential equations by Y. Pinchover Complex scaling in atomic physics: A staging ground for experimental mathematics and for extracting physics from otherwise impossible computations by W. P. Reinhardt Recent results on the Bethe-Sommerfeld conjecture by A. V. Sobolev Electric and magnetic fields, semiclassical limit: Recent developments in quantum mechanics with magnetic fields by L. Erdos Aspects of the integer quantum Hall effect by G. M. Graf Barry Simon's work on electric and magnetic fields and the semi-classical limit by I. W. Herbst Some bound state problems in quantum mechanics by D. Hundertmark.

American Mathematical Society eBooks•Jan 1, 2007•0 citations

Mathematical results in quantum mechanics : a conference on QMATH-8, Mathematical Results in Quantum Mechanics Universidad Nacional Autónoma de México, Taxco, México, December 10-14, 2001

Ricardo Weder, Pavel Exner, Benoît Grébert

Blow-up for Schrodinger equation with pointwise nonlinearity by R. Adami Quantum electrodynamics of relativistic bound states with cutoffs. II by J.-M. Barbaroux, M. Dimassi, and J.-C. Guillot Scattering by a slab: An exact calculation by F. Bentosela and M. Tater Crystalline order in one dimensional Thomas-Fermi type models by X. Blanc and C. Le Bris New results on the spectrum of lattice Schrodinger operators and applications by J. Bourgain Reconstruction of the memory from partial boundary measurements by A. L. Bukhgeim, G. V. Dyatlov, and G. Uhlmann Asymptotics for nonlinear dissipative equations in the super critical case by R. E. Cardiel and P. I. Naumkin Edge states for quantum Hall Hamiltonians by J.-M. Combes, P. D. Hislop, and E. Soccorsi A semiclassical approach in linear response theory by M. Combescure and D. Robert Wigner-von Neumann-like potentials by J. Cruz-Sampedro Equilibrium potentials in scattering theory by M. Demuth and A. Noll Straight quantum waveguides with combined boundary conditions by J. Dittrich and J. Kriz Perturbation theory for the quantum time-evolution in rotating potentials by V. Enss, V. Kostrykin, and R. Schrader Two dimensional Pauli operator via scalar potential by L. Erdos and V. Vougalter A max-min principle for the ground state of the Dirac-Fock functional by M. J. Esteban and E. Sere On the regularity of the density of electronic wave functions by S. Fournais, M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof, and T. O. Sorensen Enhanced binding through coupling to a photon field by C. Hainzl The large radius limit for coherent states on spheres by B. C. Hall and J. J. Mitchell Quantum scattering for potentials homogeneous of degree zero by I. Herbst and E. Skibsted Existence of the density of states for one-dimensional alloy-type potentials with small support by W. Kirsch and I. Veselic Statistical ensembles and density of states by V. Kostrykin and R. Schrader The Cauchy problem for the Toda lattice with a class of non-stabilized initial data by M. Kudryavtsev Absolutely continuous spectrum of Jacobi matrices by A. Laptev, S. Naboko, and O. Safronov Stability of matter in relativistic quantum electrodynamics by E. H. Lieb and M. Loss The algebra of observables in a magnetic field by M. Mantoiu and R. Purice Recent developments in value distribution theory for Schrodinger operators on the half line by D. B. Pearson Long time propagation results in quantum mechanics by D. Robert Comments on adiabatic quantum algorithms by M. B. Ruskai Tunneling destruction for a nonlinear Schrodinger equation by A. Sacchetti Symmetry breaking in a model of a rotating Bose gas by R. Seiringer Euler's constant in Segal-Bargmann analysis by S. B. Sontz Maxwell with a touch of Schrodinger by A. Tip Exponentially accurate semiclassical asymptotics by J. H. Toloza Some properties of the eigenvalues of a Schrodinger equation with energy-dependent potential by C. van der Mee and V. Pivovarchik The Bargmann transform for $L^2(S^3)$ and regularization of the Kepler problem by C. Villegas-Blas Schrodinger equations with superquadratic potentials by K. Yajima and G. Zhang Band spectrum of the Laplacian on a slab with the Dirichlet boundary condition on a grid by K. Yoshitomi Other talks Participants.

American Mathematical Society eBooks•Jan 1, 2002•0 citations

Scattering theory in mathematical physics : proceedings of the NATO Advanced Study Institute held at Denver, Colo.,U.S.A, June 11-29, 1973

James A. LaVita, Jean-Paul Marchand

These proceedings contain lectures given at the N.A.T.O. Advanced Study Institute entitled Scattering Theory in Mathematics and Physics held in Denver, Colorado, June 11-29, 1973. We have assembled the main series of lectures and some presented by other participants that seemed naturally to complement them. Unfortunately the size of this volume does not allow for a full account of all the contributions made at the Conference; however, all present were pleased by the number and breadth of those topics covered in the informal afternoon sessions. The purpose of the meeting, as reflected in its title, was to examine the single topic of scattering theory in as many of its manifestations as possible, i.e. as a hub of concepts and techniques from both mathematics and physics. The format of all the topics presented here is mathematical. The physical content embraces classical and quantum mechanical scattering, N-body systems and quantum field theoretical models. Left out are such subjects as the so-called analytic S-matrix theory and phenomeno logical models for high energy scattering. We would like to thank the main lecturers for their excellent presentations and written summaries. They provided a focus for the exceptionally strong interaction among the participants and we hope that some of the coherence achieved is reflected in these published notes. We have made no attempt to unify notation.

D. Reidel eBooks•Jan 1, 1974•2 citations
"The proceedings of the conference is devoted mainly to the mathematically rigorous approaches to the problems of quantum mechanics. The spectral properties of Schrödinger operators, including those on regions with a boundary and their generalizations, scattering theory and resonances, time-dependent Hamiltonians and quantum chaos, problems of statistical physics like spin systems, and others are discussed."--Publisher's website
This work contains the proceedings of the International Conference on Mathematical Results in Quantum Mechanics held in Blossin, Germany, May 17-21, 1993. It aims to draw attention to the recent developments in quantum mechanics and related mathematical problems. The book features sections not only on traditional subjects such as Schroedinger and Dirac operators and generalized Schroedinger generators, but also on stochastic spectral analysis, many-body problems and statistical physics, chaos, and operator theory and its applications.
I Plenary talks.- An adiabatic theorem without a gap condition.- Two-dimensional periodic Pauli operator. The effective masses at the lower edge of the spectrum.- Spectral problems in the theory of photonic crystals.- Optimal eigenvalues for some Laplacians and Schroedinger operators depending on curvature.- The spectral shift operator.- On the scattering operator for the Schroedinger equation with a time-dependent potential.- H_2-construction and some applications.- Scattering with time periodic potentials and cyclic states.- Some geometry related to decay properties of the resolvent of a class of symmetric operators.- On some asymptotic formulas in the strong localization regime of the theory of disordered systems.- Spectral measures and category.- Quantum dots. A survey of rigorous results.- II Session talks.- A simple model of concentrated nonlinearity.- Anomalous electron trapping by magnetic flux tubes and electric current vortices.- On the absolutely continuous energy distribution of a quantum mechanical system in a bounded domain.- Some aspects of generalized contact interaction in one-dimensional quantum mechanics.- Traces and trace norms for semigroup differences...- About a resolvent formula.- The determinant anomaly in low-dimensional quantum systems.- Linear Boltzmann equation as the weak coupling limit of the random Schroedinger equation.- Coexistence of different spectral types for almost periodic Schroedinger equations in dimension one.- Dynamical localization for random Schroedinger operators and an application to the almost Mathieu operator.- On fractal structure of the spectrum for periodic point perturbations of the Schroedinger operator with a uniform magnetic field.- A Weyl-Berry formula for the scattering operator associated to self-similar potentials on the line.- Localization and Lifshitz tails for random quantum waveguides.- Birman-Schwinger analysis for bound states in a pair of parallel quantum waveguides with a semitransparent boundary.- On the absolute continuity of spectra of periodic elliptic operators.- Hardy inequalities for magnetic Dirichlet forms.- Adiabatic curvature, chaos and the deformation of Riemann surfaces.- Operator interpretation of resonances arising in spectral problems for 2 x 2 matrix Hamiltonians.- On the operator-norm convergence of the Trotter-Kato product formula.- A particular case of the inverse problem for the Sturm-Liouville equation with parameter dependent potential.- One-dimensional Schroedinger operators with decaying potentials.- Stability of limiting absorption under singular perturbations.- Existence of averaging integrals for self-adjoint operators.- Monotonicity versus non-monotonicity in random operators.- A model in perturbation theory.- Band gap of the spectrum in periodically curved quantum waveguides.- A list of other talks.- A list of participants.
1. Schroedinger operators : spectra, scattering and semiclassical behaviour.- Negative discrete spectrum of the Schroedinger operator with large coupling constant : qualitative discussion.- Discrete spectrum in the gaps of the continuous one in the large-coupling-constant limit.- On the asymptotics of discrete spectrum for the Schroedinger operator in electric and homogeneous magnetic fields.- Asymptotics of the discrete spectrum of Hamiltonians of quantum systems with a homogeneous magnetic field.- Asymptotics of eigenvalues for many-particle Hamiltonians at symmetry subspaces.- Spectral asymptotics with highly accurate remainder estimates.- Bound states and resonances in quantum wires.- Spectral properties of the operators H? = ??XX + p(x)? + v(?x), p is periodic.- Discrete spectrum for a periodic Schroedinger operator perturbed by a decreasing potential.- On a complete description of the principal discrete series of spectral invariants of the Hill operator.- WKB-approximations from the perturbation theory viewpoint.- Moving potentials and the completeness of wave operators. Part II : Propagating observables on scattering states.- Representation of the three-body S-matrix in terms of effective amplitudes.- A three-body one-dimensional system with increasing interaction : wave function asymptotics.- Surprises of quantum tunneling (something about the velocity of sub-barrier motion).- 2. Point and contact interactions, self-adjoint extensions.- Lifshitz tails and non-Lifshitz tails for one-dimensional random point interactions.- Point interactions with an internal structure as limits of nonlocal point interactions.- Green's function for the Aharonov-Bohm effect with a non-Abelian gauge group.- A model of zero-width slits and the real diffraction problem.- Construction of an inelastic scatterer in nanoelectronics by the extension-theory methods.- On boundary theory for Schroedinger operators and stochastic processes.- Dirac Hamiltonian with Coulomb potential and contact intraction on a sphere.- Self-adjoint extensions of Schroedinger operators with singular potentials.- Currents and the extension theory.- 3. Quantum chaos.- Chaotic quantum billiards.- Relevance of the localization to quasienergy statistics in quantum chaotic systems.- Singular continuous quasi-energy spectrum in the kicked rotator with separable perturbation : onset of quantum chaos ?.- Relation between correlation functions and spectrum statistics in the region of quantum chaos.- 4. Other topics.- Localization effects in non-homogeneous dielectrics.- A self-adjoint dilation of the linear Boltzmann operator.- Kato problem for functional-differential equations and difference Schroedinger operators.- An existence theorem for some nonlinear nonlocal Schroedinger operators and the solitonlike dynamics for the corresponding dynamical systems.- The Sturm-Liouville problem with a potential linear in spectral parameter.- Stochastic model of tree growth.- Critical phenomenon in the stationary model of random growth.- On a quantum-classical connection, hidden symmetries and a model of Josephson junction.- Open multiquantum systems. Method of a generating functional.- Generalized functions and their applications.- List of unpublished contributions.- List of participants.
Quantum field theory, statistical mechanics: Perspectives in statistical mechanics by M. Aizenman Coherent infrared representations in non-relativistic QED by T. Chen and J. Frohlich Quantum spin systems after DLS 1978 by B. Nachtergaele Barry Simon's contributions to quantum field theory by L. Rosen Nonrelativistic two-body and NNN-body quantum systems, resonances: Isoperimetric inequalities for eigenvalues of the Laplacian by M. S. Ashbaugh and R. D. Benguria Non-self-adjoint operators and pseudospectra by E. B. Davies Barry Simon's contribution to non-relativistic quantum mechanics: Two-body and NNN-body Schrodinger operators and resonances by R. Froese NNN-body quantum scattering and quantum resonances: An overview by C. Gerard Mathematical analysis of Born-Oppenheimer approximations by G. A. Hagedorn and A. Joye Perturbation theory and atomic resonances since Schrodinger's time by E. M. Harrell II On a theorem for quantum mechanical scattering theory by A. Lenard Analytic criteria in the qualitative spectral analysis of the Schrodinger operator by V. Maz'ya The spectral geometry of geometrically finite hyperbolic manifolds by P. Perry Topics in the theory of positive solutions of second-order elliptic and parabolic partial differential equations by Y. Pinchover Complex scaling in atomic physics: A staging ground for experimental mathematics and for extracting physics from otherwise impossible computations by W. P. Reinhardt Recent results on the Bethe-Sommerfeld conjecture by A. V. Sobolev Electric and magnetic fields, semiclassical limit: Recent developments in quantum mechanics with magnetic fields by L. Erdos Aspects of the integer quantum Hall effect by G. M. Graf Barry Simon's work on electric and magnetic fields and the semi-classical limit by I. W. Herbst Some bound state problems in quantum mechanics by D. Hundertmark.
Blow-up for Schrodinger equation with pointwise nonlinearity by R. Adami Quantum electrodynamics of relativistic bound states with cutoffs. II by J.-M. Barbaroux, M. Dimassi, and J.-C. Guillot Scattering by a slab: An exact calculation by F. Bentosela and M. Tater Crystalline order in one dimensional Thomas-Fermi type models by X. Blanc and C. Le Bris New results on the spectrum of lattice Schrodinger operators and applications by J. Bourgain Reconstruction of the memory from partial boundary measurements by A. L. Bukhgeim, G. V. Dyatlov, and G. Uhlmann Asymptotics for nonlinear dissipative equations in the super critical case by R. E. Cardiel and P. I. Naumkin Edge states for quantum Hall Hamiltonians by J.-M. Combes, P. D. Hislop, and E. Soccorsi A semiclassical approach in linear response theory by M. Combescure and D. Robert Wigner-von Neumann-like potentials by J. Cruz-Sampedro Equilibrium potentials in scattering theory by M. Demuth and A. Noll Straight quantum waveguides with combined boundary conditions by J. Dittrich and J. Kriz Perturbation theory for the quantum time-evolution in rotating potentials by V. Enss, V. Kostrykin, and R. Schrader Two dimensional Pauli operator via scalar potential by L. Erdos and V. Vougalter A max-min principle for the ground state of the Dirac-Fock functional by M. J. Esteban and E. Sere On the regularity of the density of electronic wave functions by S. Fournais, M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof, and T. O. Sorensen Enhanced binding through coupling to a photon field by C. Hainzl The large radius limit for coherent states on spheres by B. C. Hall and J. J. Mitchell Quantum scattering for potentials homogeneous of degree zero by I. Herbst and E. Skibsted Existence of the density of states for one-dimensional alloy-type potentials with small support by W. Kirsch and I. Veselic Statistical ensembles and density of states by V. Kostrykin and R. Schrader The Cauchy problem for the Toda lattice with a class of non-stabilized initial data by M. Kudryavtsev Absolutely continuous spectrum of Jacobi matrices by A. Laptev, S. Naboko, and O. Safronov Stability of matter in relativistic quantum electrodynamics by E. H. Lieb and M. Loss The algebra of observables in a magnetic field by M. Mantoiu and R. Purice Recent developments in value distribution theory for Schrodinger operators on the half line by D. B. Pearson Long time propagation results in quantum mechanics by D. Robert Comments on adiabatic quantum algorithms by M. B. Ruskai Tunneling destruction for a nonlinear Schrodinger equation by A. Sacchetti Symmetry breaking in a model of a rotating Bose gas by R. Seiringer Euler's constant in Segal-Bargmann analysis by S. B. Sontz Maxwell with a touch of Schrodinger by A. Tip Exponentially accurate semiclassical asymptotics by J. H. Toloza Some properties of the eigenvalues of a Schrodinger equation with energy-dependent potential by C. van der Mee and V. Pivovarchik The Bargmann transform for L2(S3)L^2(S^3)L2(S3) and regularization of the Kepler problem by C. Villegas-Blas Schrodinger equations with superquadratic potentials by K. Yajima and G. Zhang Band spectrum of the Laplacian on a slab with the Dirichlet boundary condition on a grid by K. Yoshitomi Other talks Participants.
These proceedings contain lectures given at the N.A.T.O. Advanced Study Institute entitled Scattering Theory in Mathematics and Physics held in Denver, Colorado, June 11-29, 1973. We have assembled the main series of lectures and some presented by other participants that seemed naturally to complement them. Unfortunately the size of this volume does not allow for a full account of all the contributions made at the Conference; however, all present were pleased by the number and breadth of those topics covered in the informal afternoon sessions. The purpose of the meeting, as reflected in its title, was to examine the single topic of scattering theory in as many of its manifestations as possible, i.e. as a hub of concepts and techniques from both mathematics and physics. The format of all the topics presented here is mathematical. The physical content embraces classical and quantum mechanical scattering, N-body systems and quantum field theoretical models. Left out are such subjects as the so-called analytic S-matrix theory and phenomeno logical models for high energy scattering. We would like to thank the main lecturers for their excellent presentations and written summaries. They provided a focus for the exceptionally strong interaction among the participants and we hope that some of the coherence achieved is reflected in these published notes. We have made no attempt to unify notation.