### Abstract

Original language | English |
---|---|

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

*Theoretical and Mathematical Physics*,

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

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*Theoretical and Mathematical Physics*, vol. 142, no. 3, pp. 422-430. https://doi.org/10.1007/s11232-005-0033-x

**Quantization scheme for modular q-difference equations.** / Sergeev, Sergey.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Quantization scheme for modular q-difference equations

AU - Sergeev, Sergey

PY - 2005/3

Y1 - 2005/3

N2 - 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

AB - 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

KW - Baxter equations

KW - modular dualization

KW - strong coupling regime

U2 - 10.1007/s11232-005-0033-x

DO - 10.1007/s11232-005-0033-x

M3 - Article

VL - 142

SP - 422

EP - 430

JO - Theoretical and Mathematical Physics(Russian Federation)

JF - Theoretical and Mathematical Physics(Russian Federation)

SN - 0040-5779

IS - 3

ER -