Geodesic
Quantization scheme for modular $q$-difference equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 142 (2005) no. 3, pp. 500-509

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We consider modular pairs of certain second-order $q$-difference equations. An example of such a pair is the $t$-$Q$ Baxter equations for the quantum relativistic Toda lattice in the strong coupling regime. Another example from quantum mechanics is $q$-deformation of the Schrödinger equation with a hyperbolic potential. We show that the analyticity condition for the wave function or the Baxter function leads to a set of transcendental equations for the coefficients of the potential or the transfer matrix, the solution of which is their discrete spectrum.
Keywords: Baxter equations, modular dualization, strong coupling regime. 
@article{TMF_2005_142_3_a2,
     author = {S. M. Sergeev},
     title = {Quantization scheme for modular $q$-difference equations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {500--509},
     publisher = {mathdoc},
     volume = {142},
     number = {3},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2005_142_3_a2/}
}
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S. M. Sergeev. Quantization scheme for modular $q$-difference equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 142 (2005) no. 3, pp. 500-509. http://geodesic.mathdoc.fr/item/TMF_2005_142_3_a2/