We study the existence of positive solution for the one dimensional Schrödinger equation with mixed Liouville-Weyl fractional derivatives. tD∞α(-∞Dtαu(t))+V(t)u(t)=f(u(t)),t∈Ru∈Hα(R).Furthermore, we analyse radial symmetry property of these solutions. The proof is carried out by using variational methods jointly with comparison and rearrangement argument.