We present a new approach to the problem of Bloch electrons in a magnetic field (sometimes called the Asbel-Hofstadter problem), 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 a solution for the isotropic problem. We also present a class of solvable quasiperiodic equations related to U q(sl 2).