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

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

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/tmf1787
• https://doi.org/10.4213/tmf1787
• http://mi.mathnet.ru/eng/tmf/v142/i2/p346

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

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
2. Nikolai Iorgov, “Eigenvectors of Open Bazhanov–Stroganov Quantum Chain”, SIGMA, 2 (2006), 019, 10 pp.
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.
4. Kozlowski K.K., “Aspects of the Inverse Problem for the Toda Chain”, J. Math. Phys., 54:12 (2013), 121902
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