AN EXTENDED Q-DEFORMED SU(2) ALGEBRA AND THE BLOCH ELECTRON PROBLEM

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 function al Bethe ansatz equations whose solutions should be functions of finit e degree. It is also shown that the zero energy solution is expressed in terms of an Askey-Wilson polynomial. (C) 1998 Elsevier Science B.V.