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.
|Journal||Journal of physics: Conference series|
|Publication status||Published - 2006|
|Event||Symmetry and Structural Properties of Condesed Matter, SSPCM 2005 - Myczkowce, Poland|
Duration: 31 Aug 2005 → 7 Sep 2005
Caspers, W. J., Labuz, M., & Wal, A. (2006). On the completeness of the set of Bethe-Hulthén solutions of the linear Heisenberg system. Journal of physics: Conference series, 30, 73-85. https://doi.org/10.1088/1742-6596/30/1/011