The periodic Toda chain and a matrix generalization of the Bessel function recursion relations
- 21 October 1992
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 25 (20) , 5243-5252
- https://doi.org/10.1088/0305-4470/25/20/007
Abstract
The authors obtain the quantization conditions of the periodic Toda lattice in the Baxter form: Lambda (u)Q(u)=iNQ(u+i)+i-NQ(u-i) Lambda is the 'transfer matrix' containing the information about the spectrum and Q is an integral operator commuting with Lambda . The logarithms of the matrix elements of Q are the generating functions of the canonical Backlund transformation. The requirement that Q is analytic and vanishes when u goes to infinity completely determines the spectrum of Lambda .Keywords
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