Hq(4) symmetry: the linear q-harmonic oscillator based on generalized irreps of the q-deformed Heisenberg algebra

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

LARGE-ORDER PERTURBATION EXPANSIONS FOR THE CHARGED HARMONIC-OSCILLATOR

The charged oscillator, defined by the Hamiltonian H = -d2/dr2+ r2 + lambda/r in the domain [0, infinity], is a particular case of the family of spiked oscillators, which does not behave as a supersingular Hamiltonian. This problem is analysed around the three regions lambda --> infinity, lambda --> 0 and lambda --> -infinity by using Rayleigh-Ritz large-order perturbative expansions. A path is found to connect the large lambda regions with the small lambda region by means of the renormalization of the series expansions in lambda. Finally, the Riccati-Pade method is used to construct an implicit expansion around lambda --> 0 which extends to very large values of Absolute value of lambda.

Perturbative breaking of the pseudospin symmetry in the relativistic harmonic oscillator

We show that relativistic mean fields theories with scalar S, and vector V, quadratic radial potentials can generate a harmonic oscillator with exact pseudospin symmetry and positive energy bound states when S = -V. The eigenenergies are quite different from those of the non-relativistic harmonic oscillator. We also discuss a mechanism for perturbatively breaking this, symmetry by introducing a tensor potential. Our results shed light into the intrinsic relativistic nature of the pseudospin symmetry, which might be important in high density systems such as neutron stars.

Nonsingular spiked harmonic oscillator

A perturbative study of a class of nonsingular spiked harmonic oscillators defined by the Hamiltonian H= -d2/dr2 + r2 + λ/rα in the domain [0,∞] is carried out, in the two extremes of a weak coupling and a strong coupling regimes. A path has been found to connect both expansions for α near 2. © 1991 American Institute of Physics.

H-bond simulation in DNA using a harmonic oscillator isospectral potential

A harmonic oscillator isospectral potential obtained by supersymmetric algebra applied to quantum mechanics is suggested to simulate DNA H bonds. Thermic denaturation is studied with this potential.

Pseudospin and spin symmetries in the relativistic harmonic oscillator

We compute the analytical solutions of the generalized relativistic harmonic oscillator in 1+1 dimensions, including a linear pseudoscalar potential and quadratic scalar and vector potentials which have equal or opposite signs These are the conditions in which pseudospin or spin symmetries can be realized We consider positive and negative quadratic potentials and present their bound-state solutions for fermions and an-tifermions. We relate the spin-type and pseudospin-type spectra through charge conjugation and γ5 chiral transformations. Finally, we establish a relation of the solutions found with single-particle states of nuclei described by relativistic mean-field theories with tensor interactions and discuss the conditions in which one may have both nucleon and antin-ucleon bound states.

The Linear Potential Propagator via Wave Function Expansion

ABSTRACT: We evaluate the quantum propagator for the motion of a particle in a linear potential via a recently developped formalism [A.B. Nassar et al., Phys. Rev. E56, 1230, (1997)]. In this formalism, the propagator comes about as a type of expansion of the wave function over the space of the initial velocities.

A Laplace transform approach to the quantum harmonic oscillator

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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.

Root system of singular perturbations of the harmonic oscillator type operators

We analyze perturbations of the harmonic oscillator type operators in a Hilbert space H, i.e. of the self-adjoint operator with simple positive eigenvalues μ k satisfying μ k+1 − μ k ≥ Δ > 0. Perturbations are considered in the sense of quadratic forms. Under a local subordination assumption, the eigenvalues of the perturbed operator become eventually simple and the root system contains a Riesz basis.

The Harmonic Oscillator, a Review of Classical and Elementary Quantum Mechanics

The classical harmonic oscillator and an elementary discussion of the quantum mechanical solutions for the harmonic oscillator are discussed.

The Harmonic Oscillator's Frobenius Solution

The Frobenius solution to the differential equations associated with the harmonic oscillator (QM) is carried out in detail.

The Driven Harmonic Oscillator in Chemistry

The molecular dynamical simulation of the normal vibrational mode of water which involves H-O-H angle deformation, when driven by an external force, can be used to see how a driven harmonic oscillator, classically, is associated with the infra-red spectrum of water (and the absorption for this particular normal mode).

Molecular Dynamics and the Diatomic Molecule as Harmonic Oscillator and Rigid Rotor

The HCl molecule is simulated (using Maple) in its dynamics, for both vibrational (and implied) rotational motions. A discussion of the center of mass transformations involved is part of the total presentation.