Beyond conventional factorization: Non-Hermitian Hamiltonians with radial oscillator spectrum

The eigenvalue problem of the spherically symmetric oscillator Hamiltonian is revisited in the context of canonical raising and lowering operators. The Hamiltonian is then factorized in terms of two not mutually adjoint factorizing operators which, in turn, give rise to a non-Hermitian radial Hamiltonian. The set of eigenvalues of this new Hamiltonian is exactly the same as the energy spectrum of the radial oscillator and the new square-integrable eigenfunctions are complex Darboux-deformations of the associated Laguerre polynomials.Comment: 13 pages, 7 figure

Robustness of the European power grids under intentional attack

The power grid defines one of the most important technological networks of our times and sustains our complex society. It has evolved for more than a century into an extremely huge and seemingly robust and well understood system. But it becomes extremely fragile as well, when unexpected, usually minimal, failures turn into unknown dynamical behaviours leading, for example, to sudden and massive blackouts. Here we explore the fragility of the European power grid under the effect of selective node removal. A mean field analysis of fragility against attacks is presented together with the observed patterns. Deviations from the theoretical conditions for network percolation (and fragmentation) under attacks are analysed and correlated with non topological reliability measures.Comment: 7 pages, 4 figure

The supersymmetric modified Poschl-Teller and delta-well potentials

New supersymmetric partners of the modified Poschl-Teller and the Dirac's delta well potentials are constructed in closed form. The resulting one-parametric potentials are shown to be interrelated by a limiting process. The range of values of the parameters for which these potentials are free of singularities is exactly determined. The construction of higher order supersymmetric partner potentials is also investigated.Comment: 20 pages, LaTeX file, 4 eps figure

Exactly Solvable Hydrogen-like Potentials and Factorization Method

A set of factorization energies is introduced, giving rise to a generalization of the Schr\"{o}dinger (or Infeld and Hull) factorization for the radial hydrogen-like Hamiltonian. An algebraic intertwining technique involving such factorization energies leads to derive $n$-parametric families of potentials in general almost-isospectral to the hydrogen-like radial Hamiltonians. The construction of SUSY partner Hamiltonians with ground state energies greater than the corresponding ground state energy of the initial Hamiltonian is also explicitly performed.Comment: LaTex file, 21 pages, 2 PostScript figures and some references added. To be published in J. Phys. A: Math. Gen. (1998