We compare two Co/Pd multilayers with correspondingly smooth and rough interfaces. The first is a Co (1.5 nm)/Pd (2.6 nm) multilayer with a smooth interface deposited by the MBE technique, and the second is a Co (1.6 nm)/Pd (4.0 nm) multilayer with a rough interface deposited by the sputter technique. Both multilayers have almost the same perpendicular magnetic anisotropy energy, 1.15 Merg/cc for the Co (1.5 nm)/Pd (2.6 nm) multilayer and 1.20 Merg/cc for the Co (1.6 nm)/Pd (4.0 nm) multilayer, respectively. The symmetry of the wave function, which is measured using the magnetic Compton profile, is almost the same for both multilayers. This suggests that the smooth interface controls the wave function and enhances the PMA energy even if the Co/Pd multilayer has a thinner Pd layer.