  We construct an explicit Harish-Chandra isomorphism, from the quantum
Hamiltonian reduction of the algebra D_q(GL_2) of quantum differential
operators on GL_2, to the spherical double affine Hecke algebra associated to
GL2. The isomorphism holds for all deformation parameters non-zero q, t, such
that t does not equal to +/-i, and q is not a non-trivial root of unity. We
also discuss its extension to the root of unity case.
