This　paper　introduces　a　cascadic　adaptive　finite　element　method　for　nonlinear　eigenvalue　equations　arising　from　quantum　physics　following　the　multilevel　correction　strategy.　Instead　of　the　classical　scheme,　which　requires　solving　nonlinear　eigenvalue　equations　on　a　series　of　adaptive　spaces　directly,　the　new　scheme　consists　of　several　smoothing　processes　on　an　adaptive　space　sequence　and　nonlinear　eigenvalue　equations　being　solved　in　a　very　low　dimensional　space.　The　main　feature　of　the　proposed　scheme　is　that　large-scale　nonlinear　eigenvalue　problem　solving　is　avoided,　and　the　associated　smoothing　process　can　be　executed　efficiently　based　on　the　appropriate　number　of　smoothing　steps.　Thus,　efficiency　can　be　enhanced　by　the　proposed　cascadic　adaptive　method.　The　good　performance　of　the　new　finite　element　strategy　is　examined　by　various　numerical　experiments.