### 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

Original language | English |
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Pages (from-to) | 422-430 |

Number of pages | 9 |

Journal | Theoretical and Mathematical Physics |

Volume | 142 |

Issue number | 3 |

DOIs | |

Publication status | Published - Mar 2005 |

Externally published | Yes |

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## Cite this

Sergeev, S. (2005). Quantization scheme for modular q-difference equations.

*Theoretical and Mathematical Physics*,*142*(3), 422-430. https://doi.org/10.1007/s11232-005-0033-x