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Dispersion decay and scattering theory [[electronic resource] /] / Alexander Komech, Elena Kopylova
| Dispersion decay and scattering theory [[electronic resource] /] / Alexander Komech, Elena Kopylova |
| Autore | Komech A. I |
| Pubbl/distr/stampa | Hoboken, N.J., : Wiley, c2012 |
| Descrizione fisica | 1 online resource (204 p.) |
| Disciplina | 530.12/4 |
| Altri autori (Persone) | KopylovaElena <1960-> |
| Soggetto topico |
Klein-Gordon equation
Spectral theory (Mathematics) Scattering (Mathematics) |
| ISBN |
1-282-16526-7
9786613808523 1-118-38288-9 1-118-38289-7 1-118-38286-2 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Dispersion Decay and Scattering Theory; CONTENTS; List of Figures; Foreword; Preface; Acknowledgments; Introduction; 1 Basic Concepts and Formulas; 1 Distributions and Fourier transform; 2 Functional spaces; 2.1 Sobolev spaces; 2.2 Agmon-Sobolev weighted spaces; 2.3 Operator-valued functions; 3 Free propagator; 3.1 Fourier transform; 3.2 Gaussian integrals; 2 Nonstationary Schrodinger Equation; 4 Definition of solution; 5 Schrödinger operator; 5.1 A priori estimate; 5.2 Hermitian symmetry; 6 Dynamics for free Schrödinger equation; 7 Perturbed Schrödinger equation
7.1 Reduction to integral equation7.2 Contraction mapping; 7.3 Unitarity and energy conservation; 8 Wave and scattering operators; 8.1 Möller wave operators: Cook method; 8.2 Scattering operator; 8.3 Intertwining identities; 3 Stationary Schrödinger Equation; 9 Free resolvent; 9.1 General properties; 9.2 Integral representation; 10 Perturbed resolvent; 10.1 Reduction to compact perturbation; 10.2 Fredholm Theorem; 10.3 Perturbation arguments; 10.4 Continuous spectrum; 10.5 Some improvements; 4 Spectral Theory; 11 Spectral representation; 11.1 Inversion of Fourier-Laplace transform 11.2 Stationary Schrödinger equation11.3 Spectral representation; 11.4 Commutation relation; 12 Analyticity of resolvent; 13 Gohberg-Bleher theorem; 14 Meromorphic continuation of resolvent; 15 Absence of positive eigenvalues; 15.1 Decay of eigenfunctions; 15.2 Carleman estimates; 15.3 Proof of Kato Theorem; 5 High Energy Decay of Resolvent; 16 High energy decay of free resolvent; 16.1 Resolvent estimates; 16.2 Decay of free resolvent; 16.3 Decay of derivatives; 17 High energy decay of perturbed resolvent; 6 Limiting Absorption Principle; 18 Free resolvent; 19 Perturbed resolvent 19.1 The case λ > 019.2 The case λ = 0; 20 Decay of eigenfunctions; 20.1 Zero trace; 20.2 Division problem; 20.3 Negative eigenvalues; 20.4 Appendix A: Sobolev Trace Theorem; 20.5 Appendix B: Sokhotsky-Plemelj formula; 7 Dispersion Decay; 21 Proof of dispersion decay; 22 Low energy asymptotics; 8 Scattering Theory and Spectral Resolution; 23 Scattering theory; 23.1 Asymptotic completeness; 23.2 Wave and scattering operators; 23.3 Intertwining and commutation relations; 24 Spectral resolution; 24.1 Spectral resolution for the Schrödinger operator; 24.2 Diagonalization of scattering operator 25 T-Operator and 5-Matrix9 Scattering Cross Section; 26 Introduction; 27 Main results; 28 Limiting amplitude principle; 29 Spherical waves; 30 Plane wave limit; 31 Convergence of flux; 32 Long range asymptotics; 33 Cross section; 10 Klein-Gordon Equation; 34 Introduction; 35 Free Klein-Gordon equation; 35.1 Dispersion decay; 35.2 Spectral properties; 36 Perturbed Klein-Gordon equation; 36.1 Spectral properties; 36.2 Dispersion decay; 37 Asymptotic completeness; 11 Wave equation; 38 Introduction; 39 Free wave equation; 39.1 Time decay; 39.2 Spectral properties; 40 Perturbed wave equation 40.1 Spectral properties |
| Record Nr. | UNINA-9910138870703321 |
Komech A. I
|
||
| Hoboken, N.J., : Wiley, c2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Dispersion decay and scattering theory / / Alexander Komech, Elena Kopylova
| Dispersion decay and scattering theory / / Alexander Komech, Elena Kopylova |
| Autore | Komech A. I |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Hoboken, N.J., : Wiley, c2012 |
| Descrizione fisica | 1 online resource (204 p.) |
| Disciplina | 530.12/4 |
| Altri autori (Persone) | KopylovaElena <1960-> |
| Soggetto topico |
Klein-Gordon equation
Spectral theory (Mathematics) Scattering (Mathematics) |
| ISBN |
9786613808523
9781282165267 1282165267 9781118382882 1118382889 9781118382899 1118382897 9781118382868 1118382862 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Dispersion Decay and Scattering Theory; CONTENTS; List of Figures; Foreword; Preface; Acknowledgments; Introduction; 1 Basic Concepts and Formulas; 1 Distributions and Fourier transform; 2 Functional spaces; 2.1 Sobolev spaces; 2.2 Agmon-Sobolev weighted spaces; 2.3 Operator-valued functions; 3 Free propagator; 3.1 Fourier transform; 3.2 Gaussian integrals; 2 Nonstationary Schrodinger Equation; 4 Definition of solution; 5 Schrödinger operator; 5.1 A priori estimate; 5.2 Hermitian symmetry; 6 Dynamics for free Schrödinger equation; 7 Perturbed Schrödinger equation
7.1 Reduction to integral equation7.2 Contraction mapping; 7.3 Unitarity and energy conservation; 8 Wave and scattering operators; 8.1 Möller wave operators: Cook method; 8.2 Scattering operator; 8.3 Intertwining identities; 3 Stationary Schrödinger Equation; 9 Free resolvent; 9.1 General properties; 9.2 Integral representation; 10 Perturbed resolvent; 10.1 Reduction to compact perturbation; 10.2 Fredholm Theorem; 10.3 Perturbation arguments; 10.4 Continuous spectrum; 10.5 Some improvements; 4 Spectral Theory; 11 Spectral representation; 11.1 Inversion of Fourier-Laplace transform 11.2 Stationary Schrödinger equation11.3 Spectral representation; 11.4 Commutation relation; 12 Analyticity of resolvent; 13 Gohberg-Bleher theorem; 14 Meromorphic continuation of resolvent; 15 Absence of positive eigenvalues; 15.1 Decay of eigenfunctions; 15.2 Carleman estimates; 15.3 Proof of Kato Theorem; 5 High Energy Decay of Resolvent; 16 High energy decay of free resolvent; 16.1 Resolvent estimates; 16.2 Decay of free resolvent; 16.3 Decay of derivatives; 17 High energy decay of perturbed resolvent; 6 Limiting Absorption Principle; 18 Free resolvent; 19 Perturbed resolvent 19.1 The case λ > 019.2 The case λ = 0; 20 Decay of eigenfunctions; 20.1 Zero trace; 20.2 Division problem; 20.3 Negative eigenvalues; 20.4 Appendix A: Sobolev Trace Theorem; 20.5 Appendix B: Sokhotsky-Plemelj formula; 7 Dispersion Decay; 21 Proof of dispersion decay; 22 Low energy asymptotics; 8 Scattering Theory and Spectral Resolution; 23 Scattering theory; 23.1 Asymptotic completeness; 23.2 Wave and scattering operators; 23.3 Intertwining and commutation relations; 24 Spectral resolution; 24.1 Spectral resolution for the Schrödinger operator; 24.2 Diagonalization of scattering operator 25 T-Operator and 5-Matrix9 Scattering Cross Section; 26 Introduction; 27 Main results; 28 Limiting amplitude principle; 29 Spherical waves; 30 Plane wave limit; 31 Convergence of flux; 32 Long range asymptotics; 33 Cross section; 10 Klein-Gordon Equation; 34 Introduction; 35 Free Klein-Gordon equation; 35.1 Dispersion decay; 35.2 Spectral properties; 36 Perturbed Klein-Gordon equation; 36.1 Spectral properties; 36.2 Dispersion decay; 37 Asymptotic completeness; 11 Wave equation; 38 Introduction; 39 Free wave equation; 39.1 Time decay; 39.2 Spectral properties; 40 Perturbed wave equation 40.1 Spectral properties |
| Record Nr. | UNINA-9910818851903321 |
|
Komech A. I
|
||
| Hoboken, N.J., : Wiley, c2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Quantum mechanics : genesis and achievements / / Alexander Komech
| Quantum mechanics : genesis and achievements / / Alexander Komech |
| Autore | Komech A. I |
| Edizione | [1st ed. 2013.] |
| Pubbl/distr/stampa | Dordrecht, : Springer Science, 2012 |
| Descrizione fisica | 1 online resource (293 p.) |
| Disciplina | 539.83 |
| Soggetto topico |
Quantum theory
Physics |
| ISBN |
1-283-90975-8
94-007-5542-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Genesis of Quantum Mechanics -- Heisenberg’s Matrix Mechanics -- Schrödinger’s Wave Mechanics -- Lagrangian Formalism -- Wave Particle Duality -- The Eigenvalue Problem -- Atom Radiation -- Scattering of Light and Particles -- Atom in Magnetic Field -- Electron Spin and Pauli Equation -- Relativistic Quantum Mechanics.- Electrodynamics and Special Relativity -- Mathematical Appendices -- Exercises -- Index. |
| Record Nr. | UNINA-9910438117903321 |
|
Komech A. I
|
||
| Dordrecht, : Springer Science, 2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||