Solution of the Bosonic and Algebraic Hamiltonians by using AIM

We apply the notion of asymptotic iteration method (AIM) to determine eigenvalues of the bosonic Hamiltonians that include a wide class of quantum optical models. We consider solutions of the Hamiltonians, which are even polynomials of the fourth order with the respect to Boson operators. We also demonstrate applicability of the method for obtaining eigenvalues of the simple Lie algebraic structures. Eigenvalues of the multi-boson Hamiltonians have been obtained by transforming in the form of the single boson Hamiltonian in the framework of AIM

N-fold Supersymmetry in Quantum Systems with Position-dependent Mass

We formulate the framework of N-fold supersymmetry in one-body quantum mechanical systems with position-dependent mass (PDM). We show that some of the significant properties in the constant-mass case such as the equivalence to weak quasi-solvability also hold in the PDM case. We develop a systematic algorithm for constructing an N-fold supersymmetric PDM system. We apply it to obtain type A N-fold supersymmetry in the case of PDM, which is characterized by the so-called type A monomial space. The complete classification and general form of effective potentials for type A N-fold supersymmetry in the PDM case are given.Comment: 18 pages, no figures; Refs. updated, typos correcte

MATCASC: A tool to analyse cascading line outages in power grids

Blackouts in power grids typically result from cascading failures. The key importance of the electric power grid to society encourages further research into sustaining power system reliability and developing new methods to manage the risks of cascading blackouts. Adequate software tools are required to better analyze, understand, and assess the consequences of the cascading failures. This paper presents MATCASC, an open source MATLAB based tool to analyse cascading failures in power grids. Cascading effects due to line overload outages are considered. The applicability of the MATCASC tool is demonstrated by assessing the robustness of IEEE test systems and real-world power grids with respect to cascading failures

A study of the bound states for square potential wells with position-dependent mass

A square potential well with position-dependent mass is studied for bound states. Applying appropriate matching conditions, a transcendental equation is derived for the energy eigenvalues. Numerical results are presented graphically and the variation of the energy of the bound states are calculated as a function of the well-width and mass.Comment: To appear in Phys. Lett. A (Present e-mail of A.G: [email protected]

Exactly solvable effective mass D-dimensional Schrodinger equation for pseudoharmonic and modified Kratzer problems

We employ the point canonical transformation (PCT) to solve the D-dimensional Schr\"{o}dinger equation with position-dependent effective mass (PDEM) function for two molecular pseudoharmonic and modified Kratzer (Mie-type) potentials. In mapping the transformed exactly solvable D-dimensional ($D\geq 2$) Schr\"{o}dinger equation with constant mass into the effective mass equation by employing a proper transformation, the exact bound state solutions including the energy eigenvalues and corresponding wave functions are derived. The well-known pseudoharmonic and modified Kratzer exact eigenstates of various dimensionality is manifested.Comment: 13 page

Position-dependent mass models and their nonlinear characterization

We consider the specific models of Zhu-Kroemer and BenDaniel-Duke in a sech$^{2}$-mass background and point out interesting correspondences with the stationary 1-soliton and 2-soliton solutions of the KdV equation in a supersymmetric framework.Comment: 8 Pages, Latex version, Two new references are added, To appear in J.Phys.A (Fast Track Communication

New approach to (quasi)-exactly solvable Schrodinger equations with a position-dependent effective mass

By using the point canonical transformation approach in a manner distinct from previous ones, we generate some new exactly solvable or quasi-exactly solvable potentials for the one-dimensional Schr\"odinger equation with a position-dependent effective mass. In the latter case, SUSYQM techniques provide us with some additional new potentials.Comment: 11 pages, no figur

Pseudo-Hermitian versus Hermitian position-dependent-mass Hamiltonians in a perturbative framework

We formulate a systematic algorithm for constructing a whole class of Hermitian position-dependent-mass Hamiltonians which, to lowest order of perturbation theory, allow a description in terms of PT-symmetric Hamiltonians. The method is applied to the Hermitian analogue of the PT-symmetric cubic anharmonic oscillator. A new example is provided by a Hamiltonian (approximately) equivalent to a PT-symmetric extension of the one-parameter trigonometric Poschl-Teller potential.Comment: 13 pages, no figure, modified presentation, 6 additional references, published versio