Semianalytic study of diamagnetism in a degenerate hydrogenic manifold

The occurrence of resonant states in regions of high potential, inferred from experiments over two decades, is traced to a familiar aspect of the diagonalization of finite Hamiltonian matrices. The diagonalization generates two sets of eigenstates localized in regions of high and low potential, respectively. These sets are related by a conjugation transformation that determines the relative numbers of set elements and the scale ratio of their eigenvalue spectra. The residual eigenstates are not localized.