Published June 1977 | Version v1
Journal article

Ground state representation of the infinite one-dimensional Heisenberg ferromagnet. Pt. 2

  • 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

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
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