difference between finite element/finite difference method

Hi together, I figured I'd like to compare the finite element and finite difference method for a 1D grid consisting of 3 points. I want to solve the eigenvalue equation Laplace Psi = E Psi. For the finite difference case, this results in an eigenvalue problem for the matrix ((-2,1,0),(1,-2,1),(0,1,-2)) with eigenvalues -2., -0.585786438, -3.414213562. However, for the finite element case (linear shape functions), I get a generalized eigenvalue problem A x = lambda B x with A=((1,-1,0),(-1,2,-1),(0,-1,1)) and B=((1/3,1/6,0),(1/6,2/3,1/6),(0,1/6,1/3)). This however gives me eigenvalues 0,3,12. I don't get it. Say, this should be the schroedinger equation, shouldn't the answers be just the same eigenvalues (i.e. energies)???