Description
Book SynopsisTable of ContentsPreface
Hilbert Spaces
Definition and elementary properties
Vector-valued functions
Subsets and dual of a Hilbert space
Measures, integrals and L p spaces
Problems
Linear Operators
The algebra B(H)
Projections and isometries
Compact operators
Unbounded operators
Multiplication operators
Resolvent and spectrum of an operator
Perturbations of self-adjoint operators
Appendix
Problems
Symmetric Operators and their Extensions
The method of the Cayley transform
Differential operators with constant coefficients
Schr¨odinger operators
Appendix
Problems
Spectral Theory of Self-Adjoint Operators
Stieltjes measures
Spectral measures
Spectral parts of a self-adjoint operator
The spectral theoremThe resolvent near the spectrum
Appendix: Proof of the Spectral Theorem
Problems
Evolution Groups and Scattering Theory
Evolution groups
Characterisation of the scattering states
Asymptotic conditionWave operators
Simple scattering systemsScattering operator
Scattering operator and S-matrix
Scattering cross sections
Bounds on scattering cross sections
Coulomb scattering
Problems
The Conjugate OperatorMethod
A simple example
The method of differential inequalities
The Mourre inequality
Application to Schr¨odinger operators
Relatively smooth operators
Higher order resolvent estimates
Some commutators
Appendix: Interpolation of operators
Problems
Further Topics in Scattering Theory
Asymptotic completeness
Flux and scattering into cones
Time-independent scattering theory
The scattering matrix
Time delay
Appendix
Problems
References
Notation Index
Subject Index
