Effects of a mixed vector-scalar screened coulomb potential for spinless particles

The problem of a spinless particle subject to a general mixing of vector and scalar screened Coulomb potentials in a two-dimensional world is analyzed and its bounded solutions are found. Some unusual results, including the existence of a bona fide solitary zero-eigenmode solution, are revealed for the Klein-Gordon equation. The cases of pure vector and scalar potentials, already analyzed in previous works, are obtained as particular cases.

Bounded solutions of neutral fermions with a screened Coulomb potential

The intrinsically relativistic problem of a fermion subject to a pseudoscalar screened Coulomb plus a uniform background potential in two-dimensional space-time is mapped into a Sturm-Liouville. This mapping gives rise to an effective Morse-like potential and exact bounded solutions are found. It is shown that the uniform background potential determinates the number of bound-state solutions. The behaviour of the eigenenergies as well as of the upper and lower components of the Dirac spinor corresponding to bounded solutions is discussed in detail and some unusual results are revealed. An apparent paradox concerning the uncertainty principle is solved by recurring to the concepts of effective mass and effective Compton wavelength. (c) 2005 Elsevier B.V. All rights reserved.

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.

Unified treatment of mixed vector-scalar screened Coulomb potentials for fermions

The problem of a fermion subject to a general mixing of vector and scalar screened Coulomb potentials in a two-dimensional world is analyzed and quantization conditions are found.

Bound states by a pseudoscalar Coulomb potential in one-plus-one dimensions

The Dirac equation is solved for a pseudoscalar Coulomb potential in a two-dimensional world. An infinite sequence of bounded solutions are obtained. These results are in sharp contrast with those ones obtained in 3 + 1 dimensions where no bound-state solutions are found. Next the general two-dimensional problem for pseudoscalar power-law potentials is addressed consenting us to conclude that a nonsingular potential leads to bounded solutions. The behaviour of the upper and lower components of the Dirac spinor for a confining linear potential nonconserving- as well as conserving-parity, even if the potential is unbounded from below, is discussed in some detail. (C) 2003 Elsevier B.V. All rights reserved.

EXPLICIT SOLUTIONS FOR TRUNCATED COULOMB POTENTIAL OBTAINED FROM SUPERSYMMETRY

The Schrodinger equation with the truncated Coulomb potential is solved using the supersymmetric quantum mechanics formalism, with and without the cutoff in the angular momentum potential. We obtain some analytical eigenfunctions and eigenvalues for particular values of the cutoff parameter.

Vibrational-rotational structure of supersingular plus Coulomb potential A/r4 - Z/r*

The vibrational-rotational states of the supersingular plus Coulomb potential A/r4 - Z/r are variationally constructed using a nonorthogonal basis of atomic hydrogenic eigenfunctions modulated by an exponential factor exp(- α/r), ensuring the correct behavior in the vicinity of the supersingularity. The construction is carried out in two successive stages. The first stage is restricted to trial functions without radial nodes, leading to a variational optimization of the parameters of the basis for each value of the angular momentum. The second stage uses the complete basis to construct linear trial functions and to formulate the variational problem in terms of secular equations, yielding the successive vibrational and rotational states. Numerical results for the corresponding energy levels are presented for different combinations of the intensity parameters of the potential. © 2001 Plenum Publishing Corporation.

Pseudospin and spin symmetries in 1+1 dimensions: the case of the Coulomb potential

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

MONTE-CARLO SIMULATION OF POLYAMPHOLYTE CHAINS

Polyampholyte copolymers containing both positive and negative monomers regularly dispersed along the chain were studied. The Monte Carlo method was used to simulate chains with charged monomers interacting by screened Coulomb potential. The neutral polyampholyte chains collapse due to the attractive electrostatic interactions. The nonneutral chains are in extended conformations due to the repulsive polyelectrolyte effects that dominate the attractive polyampholyte interactions. The results are in good agreement with experiment.

Continuum resonances with shielded Coulomb-like potential and Efimov effect

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

Study of the (D)over-barN Interaction in a QCD Coulomb Gauge Quark Model

We study the (D) over barN interaction at low energies with a quark model inspired in the QCD Hamiltonian in Coulomb gauge. The model Hamiltonian incorporates a confining Coulomb potential extracted from a self-consistent quasiparticle method for the gluon degrees of freedom, and transverse-gluon hyperfine interaction consistent with a finite gluon propagator in the infrared. Initially a constituent-quark mass function is obtained by solving a gap equation and baryon and meson bound-states are obtained in Fock space using a variational calculation. Next, having obtained the constituent-quark masses and the hadron waves functions, an effective meson-nucleon interaction is derived from a quark-interchange mechanism. This leads to a short range meson-baryon interaction and to describe long-distance physics vector- and scalar-meson exchanges described by effective Lagrangians are incorporated. The derived effective (D) over barN potential is used in a Lippmann-Schwinger equation to obtain phase shifts. The results are compared with a recent similar calculation using the nonrelativistic quark model.

Quark matter in a QCD Coulomb gauge quark model

In this communication we present results of a study of chiral symmetry in quark matter using an effective Coulomb gauge QCD Hamiltonian. QCD in Coulomb gauge is convenient for a variational approach based on a quasiparticle picture for the transverse gluons, in which a confining Coulomb potential arises naturally. We show that such an effective Hamiltonian predicts chiral restoration at too low quark densities. Possible reasons for such deficiency are discussed.

Supersymmetric quantum mechanics and partially solvable potential

Supersymmetric quantum mechanics can be used to obtain the spectrum and eigenstates of one-dimensional Hamiltonians. It is particularly useful when applied to partially solvable potentials because a superalgebra allows us to compute the spectrum state by state. Some solutions for the truncated Coulomb potential, an asymptotically linear potential, and a nonpolynomial potential are shown to exemplify the method.

Gel'fand-Levitan equation for deletion of states from Coulomb spectra

The Gel'fand-Levitan formalism is used to study how a selected set of bound states can be eliminated from the spectrum of the Coulomb potential and also how to construct a bound state in the Coulomb continuum. It is demonstrated that a sizeable quantum well can be produced by deleting a large number of levels from the s spectral series and the edge of the Coulomb potential alone can support the von Neumann-Wigner states in the continuum. © 1998 Elsevier Science B.V.

Unitarity and nonrelativistic potential energy in a higher-order Lorentz symmetry breaking electromagnetic model

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)