We consider the hypothesis that dark matter (DM) and dark energy (DE) consist of ultra-light self-interacting scalar particles. It is found that the Klein–Gordon equation with only two free parameters (mass and self-coupling) on a Schwarzschild background, at the galactic length-scales has the solution which corresponds to Bose–Einstein Condensate (BEC), behaving as DM, while the constant solution at supra-galactic scales can explain DE.