Bound states of the Dirac equation for a class of effective quadratic plus inversely quadratic potentials

The Dirac equation is exactly solved for a pseudoscalar linear plus Coulomb-like potential in a two-dimensional world. This sort of potential gives rise to an effective quadratic plus inversely quadratic potential in a Sturm-Liouville problem, regardless the sign of the parameter of the linear potential, in sharp contrast with the Schrodinger case. The generalized Dirac oscillator already analyzed in a previous work is obtained as a particular case. (C) 2004 Elsevier B.V. All rights reserved.

Position-dependent effective mass Dirac equations with PT-symmetric and non-PT-symmetric potentials

We present a new procedure to construct the one-dimensional non-Hermitian imaginary potential with a real energy spectrum in the context of the position-dependent effective mass Dirac equation with the vector-coupling scheme in 1 + 1 dimensions. In the first example, we consider a case for which the mass distribution combines linear and inversely linear forms, the Dirac problem with a PT-symmetric potential is mapped into the exactly solvable Schrodinger-like equation problem with the isotonic oscillator by using the local scaling of the wavefunction. In the second example, we take a mass distribution with smooth step shape, the Dirac problem with a non-PT-symmetric imaginary potential is mapped into the exactly solvable Schrodinger-like equation problem with the Rosen-Morse potential. The real relativistic energy levels and corresponding wavefunctions for the bound states are obtained in terms of the supersymmetric quantum mechanics approach and the function analysis method.

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.

Orthogonality criterion for banishing hydrino states from standard quantum mechanics

Orthogonality criterion is used to show in a very simple and general way that anomalous bound-state solutions for the Coulomb potential (hydrino states) do not exist as bona fide solutions of the Schrodinger, Klein-Gordon and Dirac equations. (C) 2007 Elsevier B.V. All rights reserved.

Extension of PT-symmetric quantum mechanics to the Dirac theory with position-dependent mass

We present a new method to construct the exactly solvable PT-symmetric potentials within the framework of the position-dependent effective mass Dirac equation with the vector potential coupling scheme in 1 + 1 dimensions. In order to illustrate the procedure, we produce three PT-symmetric potentials as examples, which are PT-symmetric harmonic oscillator-like potential, PT-symmetric potential with the form of a linear potential plus an inversely linear potential, and PT-symmetric kink-like potential, respectively. The real relativistic energy levels and corresponding spinor components for the bound states are obtained by using the basic concepts of the supersymmetric quantum mechanics formalism and function analysis method. (C) 2007 Elsevier B.V. All rights reserved.

Bound states of bosons and fermions in a mixed vector-scalar coupling with unequal shapes for the potentials

The Klein - Gordon and the Dirac equations with vector and scalar potentials are investigated under a more general condition, V(v) + V(s) = constant. These intrinsically relativistic and isospectral problems are solved in the case of squared hyperbolic potential functions and bound states for either particles or antiparticles are found. The eigenvalues and eigenfuntions are discussed in some detail and the effective Compton wavelength is revealed to be an important physical quantity. It is revealed that a boson is better localized than a fermion when they have the same mass and are subjected to the same potentials.

Dirac's hole theory versus quantum field theory

Dirac's hole theory and quantum field theory are usually considered equivalent to each other. The equivalence, however, does not necessarily hold, as we discuss in terms of models of a certain type. We further suggest that the equivalence may fail in more general models. This problem is closely related to the validity of the Pauli principle in intermediate states of perturbation theory.

Kerr-Newman solution as a Dirac particle

For m(2) < a(2) + q(2), with m, a, and q respectively the source mass, angular momentum per unit mass, and electric charge, the Kerr-Newman (KN) solution of Einstein's equation reduces to a naked singularity of circular shape, enclosing a disk across which the metric components fail to be smooth. By considering the Hawking and Ellis extended interpretation of the KN spacetime, it is shown that, similarly to the electron-positron system, this solution presents four inequivalent classical states. Making use of Wheeler's idea of charge without charge, the topological structure of the extended KN spatial section is found to be highly non-trivial, leading thus to the existence of gravitational states with half-integral angular momentum. This property is corroborated by the fact that, under a rotation of the space coordinates, those inequivalent states transform into themselves only after a 4π rotation. As a consequence, it becomes possible to naturally represent them in a Lorentz spinor basis. The state vector representing the whole KN solution is then constructed, and its evolution is shown to be governed by the Dirac equation. The KN solution can thus be consistently interpreted as a model for the electron-positron system, in which the concepts of mass, charge and spin become connected with the spacetime geometry. Some phenomenological consequences of the model are explored.

Trajectory of virtual, bound and resonant Efimov states

The pole trajectory of Efimov states for a three-body alpha alpha beta system with alpha alpha unbound and alpha beta bound is calculated using a zero-range Dirac-delta potential. It is shown that a three-body bound state turns into a virtual one by increasing the alpha beta binding energy. This result is consistent with previous results for three equal mass particles. The present approach considers the n-n-(18)C halo nucleus. However, the results have good perspective to be tested and applied in ultracold atomic systems, where one can realize such three-body configuration with tunable two-body interaction.

Comments on spin operators and spin-polarization states of 2+1 fermions

In this brief article we discuss spin-polarization operators and spin-polarization states of 2 + 1 massive Dirac fermions and find a convenient representation by the help of 4-spinors for their description. We stress that in particular the use of such a representation allows us to introduce the conserved covariant spin operator in the 2 + 1 field theory. Another advantage of this representation is related to the pseudoclassical limit of the theory. Indeed, quantization of the pseudoclassical model of a spinning particle in 2 + 1 dimensions leads to the 4-spinor representation as the adequate realization of the operator algebra, where the corresponding operator of a first-class constraint, which cannot be gauged out by imposing the gauge condition, is just the covariant operator previously introduced in the quantum theory.

Scaling limit of virtual states of triatomic systems

Natural scales determine the physics of quantum few-body systems with short-range interactions. Thus, the scaling limit is found when the ratio between the scattering length and the interaction range tends to infinity, while the ratio between the physical scales are kept fixed. From the formal point of view, the relation of the scaling limit and the renormalization aspects of a few-body model with a zero-range interaction, through the derivation of subtracted three-body T-matrix equations that are renormalization-group invariant.

Effect of inter-adatoms correlations on the local density of states of graphene

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Catching the bound states in the continuum of a phantom atom in graphene

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Scattering and bound states of fermions in the modified Hulthen potential

In the present work the scattering of a fermion in the modified Hulthen potential is considered with a general vector and scalar and we solved the Dirac equation in the one-dimensional space. The transmission and reflection coefficients are reported. The bound-state solution is also given. The study shows the asymptotic behavior of the wave function in bound-state and scattering states solutions.