First order analytic difference equations and integrable quantum systems

Journal of Mathematical Physics - Tập 38 Số 2 - Trang 1069-1146 - 1997
S. N. M. Ruijsenaars1
1Centre for Mathematics and Computer Science, P.O. Box 4079, 1009 AB Amsterdam, The Netherlands

Tóm tắt

We present a new solution method for a class of first order analytic difference equations. The method yields explicit “minimal” solutions that are essentially unique. Special difference equations give rise to minimal solutions that may be viewed as generalized gamma functions of hyperbolic, trigonometric and elliptic type—Euler’s gamma function being of rational type. We study these generalized gamma functions in considerable detail. The scattering and weight functions (u- and w-functions) associated to various integrable quantum systems can be expressed in terms of our generalized gamma functions. We obtain detailed information on these u- and w-functions, exploiting the difference equations they satisfy.

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Tài liệu tham khảo

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Journal of Mathematical Physics

Tập 38 Số 2

1069-1146

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