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Constructing quantum mechanics
Duncan, Anthony, (Professor of physics).
اطلاعات کتابشناختی
Constructing quantum mechanics
Author :
Duncan, Anthony, (Professor of physics).
Publisher :
Oxford University,
Pub. Year :
2019
Subjects :
Quantum theory.
Call Number :
QC 174 .12 .D86 2019
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فهرست مطالب
Foreword
(8)
Contents
(12)
1 Introduction
(15)
2 Background Material and Notation
(19)
2.1 Linear Systems of Ordinary Differential Equations
(19)
2.1.1 Constant Matrices: The Matrix Exponential
(23)
2.1.2 Constant Matrices: Invariant Subspacesand Estimates on Solutions
(26)
2.1.3 Periodic Matrices: Floquet Theory
(29)
2.1.4 General Matrices and Exponential Dichotomies
(33)
2.2 Elements of Functional Analysis
(34)
2.2.1 Basic Sobolev Spaces
(34)
2.2.2 Bounded and Closed Operators
(37)
2.2.3 Variational Derivatives
(38)
2.2.4 Resolvent and Spectrum
(39)
2.2.5 Adjoint and Fredholm Operators
(41)
2.3 The Point Spectrum: Sturm–Liouville Theory
(44)
2.3.1 Sturm–Liouville Operators on a Bounded Domain
(44)
2.3.2 Sturm–Liouville Operators on the Real Line
(47)
2.3.3 Examples
(47)
2.3.3.1 A Bistable Reaction–Diffusion Equation: Pulse
(47)
2.3.3.2 A Bistable Reaction–Diffusion Equation: Traveling Front
(49)
2.4 Additional Reading
(51)
3 Essential and Absolute Spectra
(52)
3.1 The Essential Spectrum: Fronts and Pulses
(52)
3.1.1 Examples
(65)
3.1.1.1 The Generalized Korteweg–de Vries Equation
(65)
3.1.1.2 Exponentially Weighted Spaces
(66)
3.1.1.3 A Bistable Reaction–Diffusion Equation: Pulse
(68)
3.1.1.4 A Bistable Reaction–Diffusion Equation: Front
(68)
3.1.1.5 The Nonlinear Schrödinger Equation
(71)
3.2 The Absolute Spectrum
(73)
3.2.1 Examples
(77)
3.2.1.1 The Generalized Korteweg–de Vries Equation
(77)
3.2.1.2 A Bistable Reaction–Diffusion Equation: Front
(78)
3.2.2 Absolute Spectrum and the Large Domain Limit
(78)
3.3 The Essential Spectrum: Periodic Coefficients
(80)
3.3.1 Example: Hill's Equation
(83)
3.4 Additional Reading
(87)
4 Asymptotic Stability of Waves in Dissipative Systems
(88)
4.1 Linear Dynamics
(90)
4.2 Systems with Symmetries
(99)
4.3 Nonlinear Dynamics
(103)
4.4 Example: Scalar Viscous Conservation Law
(112)
4.5 Example: Nonlinear Schrödinger-Type Equations
(120)
4.6 Additional Reading
(127)
5 Orbital Stability of Waves in Hamiltonian Systems
(129)
5.1 Finite-Dimensional Systems
(130)
5.2 Infinite-Dimensional Hamiltonian Systems withSymmetry
(134)
5.2.1 The Generalized Korteweg–de Vries Equation
(135)
5.2.2 General Orbital Stability Result
(148)
5.3 Eigenvalues of Constrained Self-Adjoint Operators
(160)
5.4 Additional Reading
(168)
6 Point Spectrum: Reduction to Finite-Rank EigenvalueProblems
(170)
6.1 Perturbation of an Algebraically Simple Eigenvalue
(171)
6.1.1 Example: Parametrically Forced Ginzburg–Landau Equation
(173)
6.1.2 Example: Spatially Periodic Waves of gKdV
(176)
6.2 Perturbation of a Geometrically Simple Eigenvalue
(184)
7 Point Spectrum: Linear Hamiltonian Systems
(187)
7.1 The Krein Signature and the Hamiltonian–Krein Index
(189)
7.1.1 A Finite-Dimensional Version of Theorem 7.1.5
(193)
7.1.2 Krein Signature and Bifurcation
(197)
7.1.3 The Jones–Grillakis Instability Index
(198)
7.2 Symmetry-Breaking Perturbations
(203)
7.2.1 Hamiltonian Perturbation
(203)
7.2.1.1 Perturbations of KHam
(205)
7.2.1.2 Perturbations to the Kernel of JL
(208)
7.2.1.3 Example: Hamiltonian Perturbation of NLS
(211)
7.2.2 Non-Hamiltonian Perturbations
(214)
7.2.2.1 Example: Non-Hamiltonian Perturbation of NLS
(218)
7.3 Additional Reading
(222)
8 The Evans Function for Boundary-Value Problems
(224)
8.1 Sturm–Liouville Operators
(224)
8.2 Higher-Order Operators
(234)
8.2.1 Rigorous Multiplicity Proof: mg(0)=1*
(241)
8.2.2 Rigorous Multiplicity Proof: mg(0)2*
(243)
8.3 Second-Order Systems
(246)
8.4 The Evans Function for Periodic Problems
(249)
8.4.1 Application: Spectral Properties
(252)
8.5 Additional Reading
(256)
9 The Evans Function for Sturm–Liouville Operators on the Real Line
(257)
9.1 The Whole-Line Eigenvalue Problem
(258)
9.2 Spectral Projections and the Jost Solutions
(261)
9.3 The Evans Function
(270)
9.3.1 Example: Square-Well Potential
(275)
9.3.2 Example: Reflectionless Potential
(277)
9.4 Application: The Orientation Index
(280)
9.5 Application: Edge Bifurcations
(284)
9.5.1 The =0 Problem
(286)
9.5.2 Calculation of E(0,0)
(288)
9.5.3 Calculation of E(0,0)
(292)
9.6 Application: Eigenvalue Problems on Large Intervalswith Separated Boundary Conditions
(299)
9.7 Application: Eigenvalue Problems for Periodic Problems with Large Spatial Period
(307)
9.8 Additional Reading
(311)
10 The Evans Function for nth-Order Operators on the Real Line
(313)
10.1 The Jost Matrices
(314)
10.2 The Evans Function
(322)
10.3 Application: The Orientation Index
(324)
10.3.1 Example: Generalized Korteweg–de Vries Equation
(326)
10.3.2 Example: Parametrically Forced Ginzburg–Landau Equation
(329)
10.4 Application: Edge Bifurcations
(334)
10.4.1 Example: The Nonlinear Schrödinger Equation
(336)
10.4.2 Example: A Perturbed Manakov Equation
(340)
10.5 Eigenvalue Problems on Large Intervals: Separated Boundary Conditions
(346)
10.6 Eigenvalue Problems: Periodic Coefficients with a Large Spatial Period
(349)
10.7 Additional Reading
(352)
References
(353)
Index
(366)
