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TMF, 2005, Volume 142, Number 2, Pages 346–364 (Mi tmf1787)  

This article is cited in 4 scientific papers (total in 4 papers)

Wave functions of the toda chain with boundary interaction

N. Z. Iorgov, V. N. Shadura

N. N. Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine

Abstract: We give an integral representation of the wave functions of the quantum $N$-particle Toda chain with boundary interaction. In the case of the Toda chain with a one-boundary interaction, we obtain the wave function by an integral transformation from the wave functions of the open Toda chain. The kernel of this transformation is given explicitly in terms of $\Gamma$-functions. The wave function of the Toda chain with a two-boundary interaction is obtained from the previous wave functions by an integral transformation. In this case, the difference equation for the kernel of the integral transformation admits a separation of variables. The separated difference equations coincide with the Baxter equation.

Keywords: quantum Toda chain, separation of variables, boundary interaction

DOI: https://doi.org/10.4213/tmf1787

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English version:
Theoretical and Mathematical Physics, 2005, 142:2, 289–305

Bibliographic databases:


Citation: N. Z. Iorgov, V. N. Shadura, “Wave functions of the toda chain with boundary interaction”, TMF, 142:2 (2005), 346–364; Theoret. and Math. Phys., 142:2 (2005), 289–305

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. von Gehlen G, Iorgov N, Pakuliak S, et al, “Baxter-Bazhanov-Stroganov model: separation of variables and the Baxter equation”, Journal of Physics A-Mathematical and General, 39:23 (2006), 7257–7282  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    2. Nikolai Iorgov, “Eigenvectors of Open Bazhanov–Stroganov Quantum Chain”, SIGMA, 2 (2006), 019, 10 pp.  mathnet  crossref  mathscinet  zmath
    3. Nikolai Iorgov, Vladimir Roubtsov, Vitaly Shadura, Yuri Tykhyy, “Relativistic Toda Chain with Boundary Interaction at Root of Unity”, SIGMA, 3 (2007), 013, 14 pp.  mathnet  crossref  mathscinet  zmath
    4. Kozlowski K.K., “Aspects of the Inverse Problem for the Toda Chain”, J. Math. Phys., 54:12 (2013), 121902  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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