  We present a new approach to the problem of Bloch electrons in magnetic (
sometimes called Azbel-Hofstadter problem) field, by making explicit a natural
relation between the group of magnetic translations and the quantum group
$U_{q}(sl_2)$. The approach allows us to express the "mid" band spectrum of the
model and the Bloch wave function as solutions of the Bethe-Ansatz equations
typical for completely integrable quantum systems. The zero mode wave functions
are found explicitly in terms of $q$-deformed classical orthogonal
polynomials.In this paper we present solution for the isotropic problem. We
also present a class of solvable quasiperiodic equations related to
$U_{q}(sl_2)$.
