On the completeness of the set of Bethe-Hulthén solutions of the linear Heisenberg system

W.J. Caspers; M. Labuz; A. Wal

doi:10.1088/1742-6596/30/1/011

On the completeness of the set of Bethe-Hulthén solutions of the linear Heisenberg system

W.J. Caspers, M. Labuz, A. Wal

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Abstract

In this work we formulate the standard form of the solutions of the Heisenberg chain with periodic boundary conditions and show that these solutions can be transformed into the well-known Bethe-Hulthén solutions. The standard form is found by solving the secular problem, separated according to the irreducible representations of the translation group. The relevant parameters exp(ikj) of the Bethe-Hulthén solutions are found from a set of linear equations with coefficients derived from the standard solutions. This correspondence between standard and Bethe-Hulthén solutions realizes the completeness of the Bethe-Hulthén method.

Original language	English
Pages (from-to)	73-85
Journal	Journal of physics: Conference series
Volume	30
DOIs	https://doi.org/10.1088/1742-6596/30/1/011
Publication status	Published - 2006
Event	Symmetry and Structural Properties of Condesed Matter, SSPCM 2005 - Myczkowce, Poland Duration: 31 Aug 2005 → 7 Sept 2005

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Caspers2006onFinal published version, 155 KBLicence: CC BY

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title = "On the completeness of the set of Bethe-Hulth{\'e}n solutions of the linear Heisenberg system",

abstract = "In this work we formulate the standard form of the solutions of the Heisenberg chain with periodic boundary conditions and show that these solutions can be transformed into the well-known Bethe-Hulth{\'e}n solutions. The standard form is found by solving the secular problem, separated according to the irreducible representations of the translation group. The relevant parameters exp(ikj) of the Bethe-Hulth{\'e}n solutions are found from a set of linear equations with coefficients derived from the standard solutions. This correspondence between standard and Bethe-Hulth{\'e}n solutions realizes the completeness of the Bethe-Hulth{\'e}n method.",

author = "W.J. Caspers and M. Labuz and A. Wal",

year = "2006",

doi = "10.1088/1742-6596/30/1/011",

language = "English",

volume = "30",

pages = "73--85",

journal = "Journal of physics: Conference series",

issn = "1742-6588",

publisher = "Institute of Physics (IOP)",

note = "Symmetry and Structural Properties of Condesed Matter, SSPCM 2005, SSPCM ; Conference date: 31-08-2005 Through 07-09-2005",

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TY - JOUR

T1 - On the completeness of the set of Bethe-Hulthén solutions of the linear Heisenberg system

AU - Caspers, W.J.

AU - Labuz, M.

AU - Wal, A.

PY - 2006

Y1 - 2006

N2 - In this work we formulate the standard form of the solutions of the Heisenberg chain with periodic boundary conditions and show that these solutions can be transformed into the well-known Bethe-Hulthén solutions. The standard form is found by solving the secular problem, separated according to the irreducible representations of the translation group. The relevant parameters exp(ikj) of the Bethe-Hulthén solutions are found from a set of linear equations with coefficients derived from the standard solutions. This correspondence between standard and Bethe-Hulthén solutions realizes the completeness of the Bethe-Hulthén method.

AB - In this work we formulate the standard form of the solutions of the Heisenberg chain with periodic boundary conditions and show that these solutions can be transformed into the well-known Bethe-Hulthén solutions. The standard form is found by solving the secular problem, separated according to the irreducible representations of the translation group. The relevant parameters exp(ikj) of the Bethe-Hulthén solutions are found from a set of linear equations with coefficients derived from the standard solutions. This correspondence between standard and Bethe-Hulthén solutions realizes the completeness of the Bethe-Hulthén method.

U2 - 10.1088/1742-6596/30/1/011

DO - 10.1088/1742-6596/30/1/011

M3 - Conference article

SN - 1742-6588

VL - 30

SP - 73

EP - 85

JO - Journal of physics: Conference series

JF - Journal of physics: Conference series

T2 - Symmetry and Structural Properties of Condesed Matter, SSPCM 2005

Y2 - 31 August 2005 through 7 September 2005

ER -

On the completeness of the set of Bethe-Hulthén solutions of the linear Heisenberg system

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