Skibsted E. Spectral Analysis of N-Body Schrodinger Operators...2024

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Skibsted E. Spectral Analysis of N-Body Schrodinger Operators...2024

Textbook in PDF format Preface Introduction Scope and Results Prerequisites and Organization of the Book Many-Body Schrödinger Operators, Conditions and Notation Regular upper NN-Body Schrödinger Operators Principal Example, Dynamical Nuclei upper NN-Body Schrödinger Operators with Infinite Mass Nuclei Principal Example, Fixed Nuclei Generalized upper NN-Body Schrödinger Operators Spaces, PsDOs and Notation Reduction to a One-Body Problem An Abstract Reduction Scheme Non-multiple Two-Cluster Threshold Case Multiple Two-Cluster Threshold, script upper F 1 intersection script upper F 2 equals StartSet 0 EndSetmathcalF1capmathcalF2={0} script upper F 1 intersection script upper F 2 equals StartSet 0 EndSetmathcalF1capmathcalF2={0}; the Case lamda 0 equals normal upper Sigma 2λ0=Σ2 and lamda 0 not an element of sigma Subscript p p Baseline left parenthesis upper H prime right parenthesisλ0-.25ex-.25ex-.25ex-.25exσpp(H') The Case lamda 0 element of sigma Subscript p p Baseline left parenthesis upper H prime right parenthesisλ0inσpp(H') lamda 0 element of sigma Subscript p p Baseline left parenthesis upper H prime right parenthesisλ0inσpp(H'); Non-multiple Case lamda 0 element of sigma Subscript p p Baseline left parenthesis upper H prime right parenthesisλ0inσpp(H'); Multiple Case Multiple Two-Cluster Case, script upper F 1 intersection script upper F 2 not equals StartSet 0 EndSetmathcalF1capmathcalF2neq{0} script upper F 1 intersection script upper F 2 not equals StartSet 0 EndSetmathcalF1capmathcalF2neq{0}; a General Approach Spectral Analysis of upper H primeH' Near lamda 0λ0 Mourre Estimate Proof of Proposition 4.3 Multiple Commutators and Calculus Computing a Commutator Positive Commutator Estimates A Rellich-Type Theorem LAP Bound Microlocal Bounds and LAP Rellich-Type Theorems The Case lamda 0 equals normal upper Sigma 2λ0=Σ2 Extended Eigentransform for lamda 0 equals normal upper Sigma 2λ0=Σ2 Attractive Slowly Decaying Effective Potentials Repulsive Slowly Decaying Effective Potentials Homogeneous Degree negative 2-2 Effective Potentials The Case lamda 0 greater than normal upper Sigma 2λ0>Σ2 Extended Eigentransform for lamda 0 greater than normal upper Sigma 2λ0>Σ2 Attractive Slowly Decaying Effective Potentials Repulsive Slowly Decaying Effective Potentials Homogeneous Degree negative 2-2 Effective Potentials Physical Models Resolvent Asymptotics Near a Two-Cluster Threshold Very Short-Range Effective Potentials Two-Cluster Threshold Resonances Resolvent Asymptotics Near the Lowest Threshold Resolvent Asymptotics Near Higher Two-Cluster Thresholds Repulsive Slowly Decaying Effective Potentials Resolvent Asymptotics for Physical Models Near Two-Cluster Thresholds Elastic Scattering at a Threshold Sommerfeld's Theorem, Attractive Slowly Decaying Effective Potentials Elastic Scattering at lamda 0λ0, Attractive Slowly Decaying Effective Potentials Scattering for the One-Body Problem at Zero Energy Elastic Scattering for the upper NN-Body Problem at lamda 0λ0 Elastic Scattering at lamda 0λ0, a `Geometric' Approach Elastic Scattering at normal upper Sigma 2Σ2 Scattering for Physical Models at a Two-Cluster Threshold, Case script upper A overTilde equals script upper A 1widetildemathcalA=mathcalA1 Effective script upper O left parenthesis r Superscript negative 2 Baseline right parenthesismathcalO(r-2) Potentials, Atom–Ion Case Non-transmission at a Threshold for Physical Models Criteria for Non-transmission Proof of (8.3), Case (I) Proof of (8.3), Case (II) Proof of (8.3), Case (III) An Example of Transmission Threshold Behaviour of Cross-Sections in Atom–Ion Scattering Finiteness of Total Cross-Sections in Atom–Ion Scattering Total Cross-Sections at normal upper Sigma 2Σ2, Non-multiple Two-Cluster Case Total Cross-Sections at normal upper Sigma 2Σ2, Multiple Two-Cluster Case Appendix Bibliography Index