An extended q-deformed su(2) algebra and the Bloch electron problem

Details An extended q-deformed su(2) algebra and the Bloch electron problem An extended q-deformed su(2) algebra and the Bloch electron problem

1997-07-19

arxiv.org/abs/hep-th/9707172v1

Phys.Lett. A239 (1998) 21-26

Physics

High Energy Physics

High Energy Physics - Theory

11 pages, Latex

Scientific paper

10.1016/S0375-9601(97)00939-0

It is shown that an extended q-deformed $su(2)$ algebra with an extra (``Schwinger '') term can describe Bloch electrons in a uniform magnetic field with an additional periodic potential. This is a generalization of the analysis of Bloch electrons by Wiegmann and Zabrodin. By using a representation theory of this q-deformed algebra, we obtain functional Bethe ansatz equations whose solutions should be functions of finite degree. It is also shown that the zero energy solution is expressed in terms of an Askey Wilson polynomial.

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