3-BODY COLLAPSE FOR TABAKIN POTENTIALS AND THE THOMAS EFFECT

A system constituted of three bosons interacting via two-body separable potentials with fixed two-boson binding is known to lead to bound-state collapse in the case where the potential parameters allow two-boson S-matrix poles close to (resonance) and on (continuum bound state) the real momentum axis. The collapse is shown to be accompanied by an increase in the average kinetic energy of the two-body bound state, which signals a decrease in the range of the two-body interaction for fixed two-body binding. The collapse is claimed to be a manifestation of the well-known Thomas effect which leads to a collapse of the three-body system when the range of the two-body interaction goes to zero for a fixed two-body binding.

Supersymmetric variational energies of 3d confined potentials

Within the approach of supersymmetric quantum mechanics associated with the variational method a recipe to construct the superpotential of three-dimensional confined potentials in general is proposed. To illustrate the construction, the energies of the harmonic oscillator and the Hulthen potential, both confined in three dimensions are evaluated. Comparison with the corresponding results of other approximative and exact numerical results is presented. (C) 2003 Elsevier B.V. All rights reserved.

Nonperturbative approach to potentials in impenetrable boxes based on quasi-exact solvability

In this work we develop an approach to obtain analytical expressions for potentials in an impenetrable box. In this kind of system the expression has the advantage of being valid for arbitrary values of the box length, and respect the correct quantum limits. The similarity of this kind of problem with the quasi exactly solvable potentials is explored in order to accomplish our goals. Problems related to the break of symmetries and simultaneous eigenfunctions of commuting operators are discussed.

Structure of potentials with N higgs doublets

Extensions of the standard model with N Higgs doublets are simple extensions presenting a rich mathematical structure. An underlying Minkowski structure emerges from the study of both variable space and parameter space. The former can be completely parametrized in terms of two future lightlike Minkowski vectors with spatial parts forming an angle whose cosine is -(N-1)(-1). For the parameter space, the Minkowski parametrization enables one to impose sufficient conditions for bounded below potentials, characterize certain classes of local minima, and distinguish charge breaking vacua from neutral vacua. A particular class of neutral minima presents a degenerate mass spectrum for the physical charged Higgs bosons.

Electrochemical stability of anodic titanium oxide films grown at potentials higher than 3 V in a simulated physiological solution

The cathodic behaviour of oxides formed on titanium electrodes in physiological solutions at potentials between 3 and 5 V (vs. SCE) was studied by cyclic voltammetry. In case of anodic polarization at potentials higher than 3 V (vs. SCE), a cathodic peak at similar to 0.4 V (vs. SCE) appears in the cathodic scan, which could be due to the reduction of unstable peroxides. The results show that this peak depends on the anodic potential and the oxidation time. This behaviour supposedly is due to the formation of unstable titanium peroxides like TiO3 during anodization. Based on repetitive oxidation-reduction processes can be concluded that the created amount of TiO3 inside of the TiO2 surface layer seems to be constant. (c) 2006 Elsevier Ltd. All rights reserved.

Ladder operators for subtle hidden shape-invariant potentials

Ladder operators can be constructed for all potentials that present the integrability condition known as shape invariance, satisfied by most of the exactly solvable potentials. Using the superalgebra of supersymmetric quantum mechanics, we construct the ladder operators for two exactly solvable potentials that present a subtle hidden shape invariance.

Hamiltonian hierarchy of pseudo-potentials

The general structure of the Hamiltonian hierarchy of the pseudo-Coulomb and pseudo-Harmonic potentials is constructed by the factorization method within the supersymmetric quantum mechanics (SQMS) formalism. The excited states and spectra of eigenfunctions of the potentials are obtained through the generation of the members of the hierarchy. It is shown that the extra centrifugal term added to the Coulomb and Harmonic potentials maintain their exact solvability.

PRESYNAPTIC AND POSTSYNAPTIC MECHANISMS INVOLVED IN TETANIC FADE INDUCED BY PANCURONIUM IN THE ISOLATED RAT MUSCLE

The mechanisms underlying the fade of the tetanic contraction induced by pancuronium were studied in vitro by means of myographical and electrophysiological techniques in the extensor digitorum longus muscle of the rat. Pancuronium (0.5 mu mol/l) induced a complete fade of the tetanic contraction while leaving the twitch unaffected. At the same concentration it decreased the amplitude and increased the tetanic rundown of trains of endplate potentials (e.p.ps) evoked in the frequency of 50 Hz. The electrophysiological changes induced by pancuronium were due to decreases in both quantal sizes and quantal contents of the e.p.ps. The former effect was the result of a postsynaptic competitive action and the latter of a presynaptic inhibitory action of that compound. The decrease in quantal. content affected the e.p.ps starting from the first in the train and became larger during the generation of the sequence of e.p.ps. This intensified their tetanic rundown. It is concluded that the fade of the tetanic contraction induced by pancuronium is due to a summation of pre- and postsynaptic actions and, therefore, not only to an increase in the tetanic rundown of e.p.ps. Possible explanations for the distinct abilities of neuromuscular blockers in affecting tetani and twitches in a differential manner are also discussed.

GENERAL POTENTIALS DESCRIBED BY SO(2,1) DYNAMIC ALGEBRA IN PARABOLIC-COORDINATE SYSTEMS

We propose general three-dimensional potentials in rotational and cylindrical parabolic coordinates which are generated by direct products of the SO(2, 1) dynamical group. Then we construct their Green functions algebraically and find their spectra. Particular cases of these potentials which appear in the literature are also briefly discussed.

Barrier penetration for supersymmetric shape-invariant potentials

Exact reflection and transmission coefficients for supersymmetric shape-invariant potentials barriers are calculated by an analytical continuation of the asymptotic wavefunctions obtained via the introduction of new generalized ladder operators. The general form of the wavefunction is obtained by the use of the F(-infinity, +infinity)-matrix formalism of Froman and Froman which is related to the evolution of asymptotic wavefunction coefficients.

GROUND-STATE-ENERGY OF SINGULAR POTENTIALS

It is shown that for singular potentials of the form lambda/r(alpha),the asymptotic form of the wave function both at r --> infinity and r --> 0 plays an important role. Using a wave function having the correct asymptotic behavior for the potential lambda/r(4), it is, shown that it gives the exact ground-state energy for this potential when lambda --> 0, as given earlier by Harrell [Ann. Phys. (NY) 105, 379 (1977)]. For other values of the coupling parameter X, a trial basis;set of wave functions which also satisfy the correct boundary conditions at r --> infinity and r --> 0 are used to find the ground-state energy of the singular potential lambda/r(4) It is shown that the obtained eigenvalues are in excellent agreement with their exact ones for a very large range of lambda values.

Completeness of coherent states associated with self-similar potentials and Ramanujan's integral extension of the beta function

A decomposition of identity is given as a complex integral over the coherent states associated with a class of shape-invariant self-similar potentials. There is a remarkable connection between these coherent states and Ramanujan's integral extension of the beta function.