Published June 1977
| Version v1
Journal article
Ground state representation of the infinite one-dimensional Heisenberg ferromagnet. Pt. 2
Creators
- 1. University of Southern California, Los Angeles (USA). Dept. of Mathematics
- 2. Virginia Univ., Charlottesville (USA). Dept. of Mathematics
Description
In its ground state representation, the infinite, spin 1/2 Heisenberg chain provides a model for spin wave scattering, which entails many features of the quantum mechanical N-body problem. Here, we give a complete eigenfunction expansion for the Hamiltonian of the chain in this representation, for all numbers of spin waves. Our results resolve the questions of completeness and orthogonality of the eigenfunctions given by Bethe for finite chains, in the infinite volume limit. (orig.)
Abstract (German)
In der Grundzustandsdarstellung stellt die unendliche Heisenberg-Kette mit Spin 1/2 ein Modell der Spinwellenstreuung dar, das viele Eigenschaften des quantenmechanischen N-Koerperproblems enthaelt. In dieser Darstellung wird fuer den Hamiltonoperator der Kette eine vollstaendige Entwicklung der Eigenfunktion fuer jede Anzahl von Spinwellen angegeben. Diese Ergebnisse loesen das Problem der Vollstaendigkeit und Ortogonalitaet der von Bethe fuer endliche Ketten angegebenen Eigenfunktionen im Grenzfall unendlichen Volumens. (orig.)Additional details
Additional titles
- Subtitle (English)
- An explicit Plancherel formula
Identifiers
- DOI
- 10.1007/bf01614088;
Publishing Information
- Journal Title
- Communications in Mathematical Physics
- Journal Volume
- 54
- Journal Issue
- 3
- Series
- Commun. Math. Phys.
- Journal Page Range
- 255-278
- ISSN
- 0010-3616
INIS
- Country of Publication
- Germany
- Country of Input or Organization
- Germany
- INIS RN
- 9366243
- Subject category
- S71: CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS;
- Descriptors DEI
- EIGENFUNCTIONS; FERROMAGNETISM; GROUND STATES; HEISENBERG MODEL; MANY-BODY PROBLEM; SCATTERING; SPIN WAVES
- Descriptors DEC
- CRYSTAL MODELS; ENERGY LEVELS; FUNCTIONS; MAGNETISM; MATHEMATICAL MODELS
Optional Information
- Notes
- 8 refs.; Updated automatically by Metadata and Full-Text Enrichment Agent