Solvable Models in Quantum Mechanics
Next to the harmonic oscillator and the Coulomb potential the class of two-body models with point interactions is the only one where complete solutions are available. All mathematical and physical quantities can be calculated explicitly which makes this field of research important also for more comp...
| Main Authors: | , , , |
|---|---|
| Format: | eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1988, 1988
|
| Edition: | 1st ed. 1988 |
| Series: | Theoretical and Mathematical Physics
|
| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- I The One-Center Point Interaction
- I.1 The One-Center Point Interaction in Three Dimensions
- I.2 Coulomb Plus One-Center Point Interaction in Three Dimensions
- I.3 The One-Center ?-Interaction in One Dimension
- I.4 The One-Center ??-Interaction in One Dimension
- I.5 The One-Center Point Interaction in Two Dimensions
- II Point Interactions with a Finite Number of Centers
- II.1 Finitely Many Point Interactions in Three Dimensions
- II.2 Finitely Many ?-Interactions in One Dimension
- II.3 Finitely Many ??-Interactions in One Dimension
- II.4 Finitely Many Point Interactions in Two Dimensions
- III Point Interactions with Infinitely Many Centers
- III.1 Infinitely Many Point Interactions in Three Dimensions
- III.2 Infinitely Many ?-Interactions in One Dimension
- III.3 Infinitely Many ??-Interactions in One Dimension
- III.4 Infinitely Many Point Interactions in Two Dimensions
- III.5 Random Hamiltonians with Point Interactions
- Appendices
- A Self-Adjoint Extensions of Symmetric Operators
- B Spectral Properties of Hamiltonians Defined as Quadratic Forms
- C Schrödinger Operators with Interactions Concentrated Around Infinitely Many Centers
- D Boundary Conditions for Schrödinger Operators on (0, ?)
- E Time-Dependent Scattering Theory for Point Interactions
- F Dirichlet Forms for Point Interactions
- G Point Interactions and Scales of Hilbert Spaces
- H Nonstandard Analysis and Point Interactions
- H.1 A Very Short Introduction to Nonstandard Analysis
- H.2 Point Interactions Using Nonstandard Analysis
- I Elements of Probability Theory
- J Relativistic Point Interactions in One Dimension
- References