Formalismo canônico da mecânica clássica: alicerce da mecânica quântica

We present a succinct review of the canonical formalism of classical mechanics, followed by a brief review of the main representations of quantum mechanics. We emphasize the formal similarities between the corresponding equations. We notice that these similarities contributed to the formulation of quantum mechanics. Of course, the driving force behind the search of any new physics is based on experimental evidence

Potenciais singulares na equação de Schrodinger unidimensional via transformada de Laplace

The present work has as its goal to treat well known and interesting unidimensional cases from quantum mechanics through an unusual approach within this eld of physics. The operational method of Laplace transform, in spite of its use by Erwin Schrödinger in 1926 when treating the radial equation for the hydrogen atom, turned out to be forgotten for decades. However, the method has gained attention again for its use as a powerful tool from mathematical physics applied to the quantum mechanics, appearing in recent works. The method is specially suitable to the approach of cases where we have potential functions with even parity, because this implies in eigenfunctions with de ned parity, and since the domain of this transform ranges from 0 to ∞, it su ces that we nd the eigenfunction in the positive semi axis and, with the boundary conditions imposed over the eigenfunction at the origin plus the continuity (discontinuity) of the eigenfunction and its derivative, we make the odd, even or both parity extensions so we can get the eigenfunction along all the axis. Factoring the eigenfunction behavior at in nity and origin, we take the due care with the points that might bring us problems in the later steps of the solving process, thus we can manipulate the Schrödinger's Equation regardless of time, so that way we make it convenient to the application of Laplace transform. The Chapter 3 shows the methodology that must be followed in order to search for the solutions to each problem

A demonização da alma indígena: jesuítas e caraíbas na Terra de Santa Cruz

Pós-graduação em História - FCHS

Mid-infrared supercontinuum generation in a suspended-core As2S3 chalcogenide microstructured optical fiber

We demonstrate the supercontinuum (SC) generation in a suspended-core As2S3 chalcogenide microstructured optical fiber (MOF). The variation of SC is investigated by changing the fiber length, pump peak power and pump wavelength. In the case of long fibers (20 and 40 cm), the SC ranges are discontinuous and stop at the wavelengths shorter than 3500 nm, due to the absorption of fiber. In the case of short fibers (1.3 and 2.4 cm), the SC ranges are continuous and can extend to the wavelengths longer than 4 μm. The SC broadening is observed when the pump peak power increases from 0.24 to 1.32 kW at 2500 nm. The SC range increases with the pump wavelength changing from 2200 to 2600 nm, corresponding to the dispersion of As2S3 MOF from the normal to anomalous region. The SC generation is simulated by the generalized nonlinear Schrödinger equation. The simulation includes the SC difference between 1.3 and 2.4 cm long fiber by 2500 nm pumping, the variation of SC with pump peak power in 2.4 cm long fiber, and the variation of SC with pump wavelength in 1.3 cm long fiber. The simulation agrees well with the experiment.

Modelo de poços quânticos para a transferência de elétrons

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Equação de Fokker-Planck e enovelamento de proteínas

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

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 squeezed state holomorphic phase space representation of equations of motion

A mapping scheme is presented which takes quantum operators associated to bosonic degrees of freedom into complex phase space integral kernel representatives. The procedure consists of using the Schrödinger squeezed state as the starting point for the construction of the integral mapping kernel which, due to its inherent structure, is suited for the description of second quantized operators. Products and commutators of operators have their representatives explicitly written which reveal new details when compared to the usual q-p phase space description. The classical limit of the equations of motion for the canonical pair q-p is discussed in connection with the effect of squeezing the quantum phase space cellular structure. © 1993.

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.

Evaluation of effective nucleon-nucleon potential and description of α-cluster type nuclei in restricted dynamics approach

The application of the Restricted Dynamics Approach in nuclear theory, based on the approximate solution of many-particle Schrödinger equation, which accounts for all conservation laws in many-nucleon system, is discussed. The Strictly Restricted Dynamics Model is used for the evaluation of binding energies, level schemes, E2 and Ml transition probabilities as well as the electric quadrupole and magnetic dipole momenta of light a-cluster type nuclei in the region 4 ≤ A ≤ 40. The parameters of effective nucleonnucleon interaction potential are evaluated from the ground state binding energies of doubly magic nuclei 4He, 16O and 40Ca.

Eletrodinâmica de ordem superior em (2+1)D

Pós-graduação em Física - IFT

Oscilador harmônico unidimensional via transformada unilateral de Fourier e mapeamento do potencial de morse unidimensional nos potenciais pseudo-harmônico e de kratzer tridimensionais

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

Estudo de sistemas não-lineares em mecânica quântica

The main goal of this work is to investigate the effects of a nonlinear cubic term inserted in the Schrödinger equation for one-dimensional potentials studied in Quantum Mechanics textbooks. Being the main tool the numerical analysis in a large number of works, the analysis of this effect by this term in the potential itself, in order to work with an analytical solution, can be considered something new. For the harmonic oscillator potential, the analysis was made from a numerical method, comparing the result with the known results in the literature. In the case of the infinite well potential and the step potential, hoping to work with an analytical solution, by construction we started with the known wavefunction for the linear case noting the effects in the other physical quantities. The coupling of the physical quantities involved in this work has yielded, besides many complications in the calculations, a series of conditions on the existence and validity of the solutions in regard to the system possible configurations