Quantization scheme for modular q-difference equations

Sergey Sergeev

Research output: Contribution to journalArticle

2 Citations (Scopus)

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 languageEnglish
Pages (from-to)422-430
Number of pages9
JournalTheoretical and Mathematical Physics
Volume142
Issue number3
DOIs
Publication statusPublished - Mar 2005
Externally publishedYes

Fingerprint

Modular Equations
Q-difference Equations
difference equations
Quantization
Q-deformation
Toda Lattice
Discrete Spectrum
Transcendental
Analyticity
Transfer Matrix
Strong Coupling
Second Order Equations
Wave Function
Quantum Mechanics
quantum mechanics
wave functions
Coefficient
coefficients

Cite this

Sergeev, Sergey. / Quantization scheme for modular q-difference equations. In: Theoretical and Mathematical Physics. 2005 ; Vol. 142, No. 3. pp. 422-430.
@article{e495c6b55e47439d94b6f66887c21fa1,
title = "Quantization scheme for modular q-difference equations",
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 Schr{\"o}dinger 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",
author = "Sergey Sergeev",
year = "2005",
month = "3",
doi = "10.1007/s11232-005-0033-x",
language = "English",
volume = "142",
pages = "422--430",
journal = "Theoretical and Mathematical Physics(Russian Federation)",
issn = "0040-5779",
publisher = "Springer",
number = "3",

}

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

In: Theoretical and Mathematical Physics, Vol. 142, No. 3, 03.2005, p. 422-430.

Research output: Contribution to journalArticle

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 -