Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Mathematical surveys and monographs

Multiparticle Quantum Scattering in Constant Magnetic Fields

Christian Gérard, Izabella Łaba

Published Dec 4, 2001• 37 citations
Publisher

Abstract

Fundamentals Geometrical methods I The Mourre theory Basic propagation estimates Geometrical methods II Wave operators and scattering theory Open problems Appendix Bibliography Index.
DOI
10.1090/surv/090

Related papers

Quantum mechanics : for engineering, materials science, and applied physics

H. Kroemer

1. Wave-Particle Duality and Schroedinger Equation. 2. Introduction to Bound States. 3. Rotationally Invariant Potentials: Hydrogen Atom and Beyond. 4. Wave Packets and Uncertainty Relations. 5. Scattering by Simple Barriers. 6. WKB Approximations. 7. Expectation Values and Operators. 8. Electrons in a Magnetic Field. 9. Beyond Hermitian Operators. 10. Harmonic Oscillator: Full Operator Treatment. 11. Composite Systems. 12. Variational Principle. 13. Expansion Principle and Matrix Formulation. 14. Perturbation Theory, I: Degenerate Perturbation Theory. 15. Perturbation Theory, II: Non-Degenerate Perturbation Theory. 16. Symmetry. 17. Electrons in Periodic Crystal Potentials. 18. Rotational Invariance and Angular Momentum. 19. Time-Dependent Perturbation Theory. 20. Elements of Field Quantization. 21. Electron Spin. 22. Indistinguishable Particles: Fermions and Bosons. Appendices: Dirac ...d-Function. Poisson-Distributed Events. Spherical Harmonics. Hydrogen Radial Eigenfunctions. Fourier Integral. Construction of Two Group Character Tables. Selected General References. Fundamental Constants. Index.

Prentice-Hall International eBooks•Jan 1, 1994•15 citations

Scattering Theory in Quantum Mechanical Problems

Dimitri R. Yafaev

The aim of the lecture is to briefly describe the mathematical background of scattering theory for two- and three-particle quantum systems. We discuss basic objects of the theory: wave and scattering operators and the corresponding scattering matrix and illustrate them on the example of the Schrödinger equation. Our goal is to present time-dependent and stationary approaches and to describe the underlying mathematical methods. We also give a sketch of scattering theory for three interacting quantum particles including a difficult problem of the asymptotic completeness of scattering channels. Along with traditional results, we discuss new scattering channels arising for long-range pair interactions.

arXiv:2205.13204•May 26, 2022•0 citations

Quantum Physics: A Fundamental Approach to Modern Physics

M. Corcoran

Contents Light Wave Mechanics The Time-Independent Schrodinger Equation One-Dimensional Potentials Principles of Quantum Mechanics Quantum Mechanics in three Dimensions Identical Particles Solid-State Physics Nuclear Physics Particle Physics Appendix i: Special Relativity Appendix ii: Power-Series Solutions Appendix iii: Constants and Conversion Factors

•Aug 7, 2009•11 citations

Lecture Notes on Quantum Mechanics

Samuel D Lindenbaum

Failure of the classical theories wave packets wave functions and probability Schrodinger's Equation quantum mechanical operators Schrodinger's Equation with forces continuous spectrum Eigensolutions the harmonic oscillator three-dimensional problems matrices matrices in different representations approximate methods I applications of WKB method alpha decay approximate methods II continuous spectrum perturbation approximate methods III spin and spinors fine structure of the hydrogen atom anomalous Zeeman effect assemblages of identical particles the Dirac Equation non-relativistic limits of the Dirac Equation Dirac operator and wave function transformations negative energy solutions - positron theory relativistic theory of Coulomb scattering Compton scattering.

WORLD SCIENTIFIC eBooks•Apr 1, 1999•57 citations

Quantum Field Theory of Non-equilibrium States

Jørgen Rammer

Preface 1. Quantum fields 2. Operators on the multi-particle state space 3. Quantum dynamics and Green's functions 4. Non-equilibrium theory 5. Real-time formalism 6. Linear response theory 7. Quantum kinetic equations 8. Non-equilibrium superconductivity 9. Diagrammatics and generating functionals 10. Effective action 11. Disordered conductors 12. Classical statistical dynamics Appendices: A. Path integrals B. Retarded and advanced propagators C. Analytic properties of Green's functions Bibliography Index.

•Mar 1, 2011•13 citations

The field B[(3)]

Myron Wyn Evans, Jean Pierre Vigier

Preface * 1: Wave and Particle * 2: Fundamental Symmetries * 3: The Origins of Wave Mechanics * 4: Interrelation of Field Equations * 5: Transverse and Longitudinal Photons and Fields * 6: Creation and Annihilation of Photons * 7: Experimental Evidence for Ii * 8: The Concept of Photon Mass * 9: Aharonov-Bohm Effects * 10: Modifications of Lagrangian Field Theory * 11: Pseudo Four-Vector Representations of Electric and Magnetic Fields * 12: Derivation of Ii3 from the Relativistic Hamilton-Jacobi Equation of e in Amu * Appendices * References * Index.

Kluwer Academic Publishers eBooks•Jan 1, 1994•0 citations
1. Wave-Particle Duality and Schroedinger Equation. 2. Introduction to Bound States. 3. Rotationally Invariant Potentials: Hydrogen Atom and Beyond. 4. Wave Packets and Uncertainty Relations. 5. Scattering by Simple Barriers. 6. WKB Approximations. 7. Expectation Values and Operators. 8. Electrons in a Magnetic Field. 9. Beyond Hermitian Operators. 10. Harmonic Oscillator: Full Operator Treatment. 11. Composite Systems. 12. Variational Principle. 13. Expansion Principle and Matrix Formulation. 14. Perturbation Theory, I: Degenerate Perturbation Theory. 15. Perturbation Theory, II: Non-Degenerate Perturbation Theory. 16. Symmetry. 17. Electrons in Periodic Crystal Potentials. 18. Rotational Invariance and Angular Momentum. 19. Time-Dependent Perturbation Theory. 20. Elements of Field Quantization. 21. Electron Spin. 22. Indistinguishable Particles: Fermions and Bosons. Appendices: Dirac ...d-Function. Poisson-Distributed Events. Spherical Harmonics. Hydrogen Radial Eigenfunctions. Fourier Integral. Construction of Two Group Character Tables. Selected General References. Fundamental Constants. Index.
The aim of the lecture is to briefly describe the mathematical background of scattering theory for two- and three-particle quantum systems. We discuss basic objects of the theory: wave and scattering operators and the corresponding scattering matrix and illustrate them on the example of the Schrödinger equation. Our goal is to present time-dependent and stationary approaches and to describe the underlying mathematical methods. We also give a sketch of scattering theory for three interacting quantum particles including a difficult problem of the asymptotic completeness of scattering channels. Along with traditional results, we discuss new scattering channels arising for long-range pair interactions.
Failure of the classical theories wave packets wave functions and probability Schrodinger's Equation quantum mechanical operators Schrodinger's Equation with forces continuous spectrum Eigensolutions the harmonic oscillator three-dimensional problems matrices matrices in different representations approximate methods I applications of WKB method alpha decay approximate methods II continuous spectrum perturbation approximate methods III spin and spinors fine structure of the hydrogen atom anomalous Zeeman effect assemblages of identical particles the Dirac Equation non-relativistic limits of the Dirac Equation Dirac operator and wave function transformations negative energy solutions - positron theory relativistic theory of Coulomb scattering Compton scattering.
Preface 1. Quantum fields 2. Operators on the multi-particle state space 3. Quantum dynamics and Green's functions 4. Non-equilibrium theory 5. Real-time formalism 6. Linear response theory 7. Quantum kinetic equations 8. Non-equilibrium superconductivity 9. Diagrammatics and generating functionals 10. Effective action 11. Disordered conductors 12. Classical statistical dynamics Appendices: A. Path integrals B. Retarded and advanced propagators C. Analytic properties of Green's functions Bibliography Index.
Preface * 1: Wave and Particle * 2: Fundamental Symmetries * 3: The Origins of Wave Mechanics * 4: Interrelation of Field Equations * 5: Transverse and Longitudinal Photons and Fields * 6: Creation and Annihilation of Photons * 7: Experimental Evidence for Ii * 8: The Concept of Photon Mass * 9: Aharonov-Bohm Effects * 10: Modifications of Lagrangian Field Theory * 11: Pseudo Four-Vector Representations of Electric and Magnetic Fields * 12: Derivation of Ii3 from the Relativistic Hamilton-Jacobi Equation of e in Amu * Appendices * References * Index.