As before define random Hamiltonian operator H: V_n^*\to V_n^* by H = \triangle+P where P acts multiplicatively on each vertex, and \triangle is the level n pointwise laplacian, whose formula is derived in Differential Equations on Fractals. We obtain the solutions to the eigen problem Hv = \lambda v and Hu=1 via finite element method, utilizing the biharmonic splines space of a lower level for an approximate of the solution. We demonstrate selected eigenfunctions with varying P_{max} in the result section, included also is a plot of the eigenvalue counting function and its loglog plot.