VARIATIONAL SPIKED OSCILLATOR

A variational analysis of the spiked harmonic oscillator Hamiltonian -d2/dr2 + r2 + lambda/r5/2, lambda > 0, is reported. A trial function automatically satisfying both the Dirichlet boundary condition at the origin and the boundary condition at infinity is introduced. The results are excellent for a very large range of values of the coupling parameter lambda, suggesting that the present variational function is appropriate for the treatment of the spiked oscillator in all its regimes (strong, moderate, and weak interactions).

Variational and perturbative schemes for a spiked harmonic oscillator

A variational analysis of the spiked harmonic oscillator Hamiltonian operator - d2/dx2 + x2 + l(l + 1)/x2 + λ|x| -α, where α is a real positive parameter, is reported in this work. The formalism makes use of the functional space spanned by the solutions of the Schrödinger equation for the linear harmonic oscillator Hamiltonian supplemented by a Dirichlet boundary condition, and a standard procedure for diagonalizing symmetric matrices. The eigenvalues obtained by increasing the dimension of the basis set provide accurate approximations for the ground state energy of the model system, valid for positive and relatively large values of the coupling parameter λ. Additionally, a large coupling perturbative expansion is carried out and the contributions up to fourth-order to the ground state energy are explicitly evaluated. Numerical results are compared for the special case α = 5/2. © 1989 American Institute of Physics.

A Weak Maximum Principle for Optimal Control Problems with Nonsmooth Mixed Constraints

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Dynamical collapse in a degenerate binary fermion mixture using a hydrodynamic model

We use a time-dependent dynamical hydrodynamic model to study a collapse in a degenerate fermion-fermion mixture ( DFFM) of different atoms. Due to a strong Pauli-blocking repulsion among identical spin-polarized fermions at short distances, there cannot be a collapse for repulsive interspecies fermion fermion interaction. However, there can be a collapse for a sufficiently attractive interspecies fermion-fermion interaction in a DFFM of different atoms. Using a variational analysis and numerical solution of the hydrodynamic model, we study different aspects of collapse in such a DFFM initiated by a jump in the interspecies fermion-fermion interaction ( scattering length) to a large negative ( attractive) value using a Feshbach resonance. Suggestion for experiments of collapse in a DFFM of distinct atoms is made.

Spatially-antisymmetric localization of matter wave in a bichromatic optical lattice

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Dynamics of quasi-one-dimensional bright and vortex solitons of a dipolar Bose-Einstein condensate with repulsive atomic interaction

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Localization of a dipolar Bose-Einstein condensate in a bichromatic optical lattice

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Symmetry breaking in a localized interacting binary Bose-Einstein condensate in a bichromatic optical lattice

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Matter-wave localization in a random potential

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Variational supersymmetric approach to evaluate Fokker-Planck probability

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Vibrational-rotational analysis of the Hulthen potential using hydrogenic eigenfunction bases

Hulthen's potential admits analytical solutions for its energy eigenvalues and eigenfunctions corresponding to zero orbital angular momentum stales, but its non zero angular momentum states are not equally known. This work presents a vibrational-rotational analy sis of Hulthen's potential using hydrogenic eigenfunction bases, which may be of interest and useful to students of quantum mechanics at different stages.

Stability analysis of the D-dimensional nonlinear Schrodinger equation with trap and two- and three-body interactions

Considering the static solutions of the D-dimensional nonlinear Schrodinger equation with trap and attractive two-body interactions, the existence of stable solutions is limited to a maximum critical number of particles, when D greater than or equal to 2. In case D = 2, we compare the variational approach with the exact numerical calculations. We show that, the addition of a positive three-body interaction allows stable solutions beyond the critical number. In this case, we also introduce a dynamical analysis of the conditions for the collapse. (C) 2000 Published by Elsevier B.V. B.V. All rights reserved.

On a regular convex solver potential for an elastic-damage constitutive model: a theoretical analysis

This work is related with the proposition of a so-called regular or convex solver potential to be used in numerical simulations involving a certain class of constitutive elastic-damage models. All the mathematical aspects involved are based on convex analysis, which is employed aiming a consistent variational formulation of the potential and its conjugate one. It is shown that the constitutive relations for the class of damage models here considered can be derived from the solver potentials by means of sub-differentials sets. The optimality conditions of the resulting minimisation problem represent in particular a linear complementarity problem. Finally, a simple example is present in order to illustrate the possible integration errors that can be generated when finite step analysis is performed. (C) 2003 Elsevier Ltd. All rights reserved.

Morse potential energy spectra through the variational method and supersymmetry

The Variational Method is applied within the context of Supersymmetric Quantum Mechanics to provide information about the energy and eigenfunction of the lowest levels of a Hamiltonian. The approach is illustrated by the case of the Morse potential applied to several diatomic molecules and the results are compared with stabilished results. (C) 2000 Elsevier Science B.V.

Induced variational method from supersymmetric quantum mechanics and the screened Coulomb potential

The formalism of supersymmetric quantum mechanics supplies a trial wave function to be used in the variational method. The screened Coulomb potential is analyzed within this approach. Numerical and exact results for energy eigenvalues are compared.