A Laplace transform approach to the quantum harmonic oscillator

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

VSR symmetries in the DKP algebra: The interplay between Dirac and Elko spinor fields

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Dirac gaugions, R symmetry and the 125 GeV Higgs

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

Massive spin-2 particles via embedment of the Fierz-Pauli equations of motion

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A virtual experiment for the detection of specific features in the frequency response of a coupled nonlinear and linear oscillator

This paper presents an investigation into some practical issues that may be present in a real experiment, when trying to validate the theoretical frequency response curve of a two degree-of-freedom nonlinear system consisting of coupled linear and nonlinear oscillators. Some specific features, such as detached resonance curves, have been theoretically predicted in multi degree-of-freedom nonlinear oscillators, when subject to harmonic excitation, and the system parameters have been shown to be fundamental in achieving such features. When based on a simplified model, approximate analytical expression for the frequency response curves may be derived, which may be validated by the numerical solutions. In a real experiment, however, the practical achievability of such features was previously shown to be greatly affected by small disturbances induced by gravity and inertia, which led to some solutions becoming unstable which had been predicted to be stable. In this work a practical system configuration is proposed where such effects are reduced so that the previous limitations are overcome. A virtual experiment is carried out where a detailed multi-body model of the oscillator is assembled and the effects on the system response are investigated.

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.

The Morse oscillator generalised from supersymmetry

Using the factorisation method in supersymmetric quantum mechanics the author determines new potentials from the Morse oscillator. This method is applied although the ladder operators are not used.

Approximate analytic expression for the eigenenergies of the anharmonic oscillator V(x)=Ax6+Bx2

An approximate analytic expression for the eigenenergies of the anharmonic oscillator V(x)=Ax6+Bx2 is introduced, starting from particular analytic solutions which are valid when certain relations between the parameters A and B are held. © 1995 The American Physical Society.

General method for reducing the two-body Dirac equation

A semirelativistic two-body Dirac equation with an enlarged set of phenomenological potentials, including Breit-type terms, is investigated for the general case of unequal masses. Solutions corresponding to definite total angular momentum and parity are shown to fall into two classes, each one being obtained by solving a system of four coupled first-order radial differential equations. The reduction of each of these systems to a pair of coupled Schrödinger-type equations is also discussed. © 1992 American Institute of Physics.

Algebraic solution of an anisotropic ring-shaped oscillator

Using an algebraic technique related to the SO (2, 1) group we construct the Green function for the potential ar2 + b(r sin θ)-2 + c(r cos θ)-2 + dr2 sin2θ + er2 cos2θ. The energy spectrum and the normalized wave functions are also obtained. © 1990.