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Quantization scheme for modular q-difference equations

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Abstract

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.

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Authors and Affiliations

  1. Department of Theoretical Physics, Research School of Physical Sciences and Engineering, Australian National University, Canberra, Australia

    S. M. Sergeev

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  1. S. M. Sergeev
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 142, No. 3, pp. 500–509, March, 2005.

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Sergeev, S.M. Quantization scheme for modular q-difference equations. Theor Math Phys 142, 422–430 (2005). https://doi.org/10.1007/s11232-005-0033-x

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  • DOI: https://doi.org/10.1007/s11232-005-0033-x

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