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Antonio S. de Castro

Publications and source records attributed to Antonio S. de Castro.

At least 19 recordsLinked to original sources
arXiv2026

Scattering, bound states, and resonances in the one-dimensional Dirac equation via supersymmetric quantum mechanics

We develop a unified treatment of scattering and discrete spectra for the one-dimensional Dirac equation with scalar and vector interactions. Under the spin-symmetry condition, the coupled first-order Dirac system maps exactly onto an effective Sturm--Liouville (Schrö\-din\-ger-like) problem for a single spinor component. This mapping provides a convenient framework for analyzing transmission, reflection, and analytic continuation. As an explicit application, we consider effective interactions of hyperbolic Pöschl--Teller type and exploit supersymmetric quantum mechanics and shape invariance to obtain a closed-form expression for the transmission probability. The bound-state spectrum is then recovered from the poles of the analytically continued transmission amplitude, reproducing known results and offering a unified description of scattering and bound states. For the barrier configuration, we briefly comment on the resulting pole pattern in the complex momentum plane and its connection with resonance and quasi-normal-mode behavior. Moreover, we use the chiral transformation to relate the spin- and pseudospin-symmetry sectors and translate results between them without repeating the full derivation.

quant-ph↗
arXiv2025

Effects of the Lorentz symmetry violation on relativistic neutral scalar bosons: Scattering and bound states

In this letter, we investigate the effects of Lorentz symmetry violation on a relativistic neutral scalar boson within the framework of the Klein-Gordon formalism. We consider a tensor $(K_F)_{μναβ}$ out of the Standard Model Extension, which describes the field configuration consisting of a constant magnetic field $\vec{B}=B\hat{z}$ and a cylindrical electric field $\vec{E}=\fracλ{r}\hat{r}$. We analyze and discuss the effects of Lorentz symmetry violation on the equation of motion and show that the presence of a specific Lorentz symmetry violation parameter is essential to obtain analytical solutions for scattering and bound states. Employing the partial wave approach in cylindrical coordinates, we calculate the relativistic phase shift, scattering amplitude and $S$-matrix, and discuss the effects of Lorentz symmetry violation on the phase shift. Furthermore, we obtain bound-state solutions by examining the poles of the $S$-matrix and compare our findings with those reported in the literature. Our results reveal that bound-state solutions are only feasible for a restrict range of Lorentz symmetry violation parameters, which contradict previous studies.

hep-th↗
arXiv2024

On the electromagnetic interaction and the anomalous term in the Duffin-Kemmer-Petiau theory

The problem of vectorial mesons embedded in an electromagnetic field via Duffin-Kemmer-Petiau (DKP) formalism is reinvestigated. Considering the electromagnetic interaction as a minimal coupling, an incorrect value $(g=1)$ is identified for the gyromagnetic factor ($g$-factor). Furthermore, it is shown that is cumbersome to find analytical solutions due to the presence of the so-called anomalous term for the spin-1 sector of the DKP theory. Suspecting that the anomalous term results from an incomplete version of the DKP equation to describe the electromagnetic interaction, we consider the addition of a non-minimal coupling. This leads to the correct $g$-factor $(g=2)$, and as a consequence, the anomalous term becomes proportional to an external four current. As an application, the DKP equation with a static uniform magnetic field is considered, yielding the corresponding Landau levels.

hep-th↗
arXiv2024

Remarks on the ($2+1$)-dimensional Duffin-Kemmer-Petiau oscillator in an external magnetic field

This work re-examines the issue of spin-$1$ particles in a ($2+1$)-dimensional Duffin-Kemmer-Petiau oscillator (DKPO) in the presence of an external magnetic field. By following the appropriate procedure for the spin-$1$ sector of the Duffin-Kemmer-Petiau (DKP) theory, the previously used $6\times 6$ representation in the literature is shown to be reducible to a $3\times 3$ irreducible representation. This approach enabled us to find new aspects of the results recently disseminated in various studies, as well as other considerations overlooked and requiring revision. Finally, we present some applications of two-dimensional DKP theory in condensed matter systems, particularly in Lieb lattices.

quant-ph↗
arXiv2019

Proper treatment of scalar and vector exponential potentials in the Klein-Gordon equation: Scattering and bound states

We point out a misleading treatment in the literature regarding to bound-state solutions for the $s$-wave Klein-Gordon equation with exponential scalar and vector potentials. Following the appropriate procedure for an arbitrary mixing of scalar and vector couplings, we generalize earlier works and present the correct solution to bound states and additionally we address the issue of scattering states. Moreover, we present a new effect related to the polarization of the charge density in the presence of weak short-range exponential scalar and vector potentials.

hep-th↗
arXiv2017

Relativistic quantum dynamics of scalar bosons under a full vector Coulomb interaction

The relativistic quantum dynamics of scalar bosons in the background of a full vector coupling (minimal plus nonminimal vector couplings) is explored in the context of the Duffin-Kemmer-Petiau formalism. The Coulomb phase shift is determined for a general mixing of couplings and it is shown that the space component of the nonminimal coupling is a {\it sine qua non} condition for the exact closed-form scattering amplitude. It follows that the Rutherford cross section vanishes in the absence of the time component of the minimal coupling. Bound-state solutions obtained from the poles of the partial scattering amplitude show that the time component of the minimal coupling plays an essential role. The bound-state solutions depend on the nonminimal coupling and the spectrum consists of particles or antiparticles depending on the sign of the time component of the minimal coupling without chance for pair production even in the presence of strong couplings. It is also shown that an accidental degeneracy appears for a particular mixing of couplings.

hep-th↗
arXiv2016

From the generalized Morse potential to a unified treatment of the $D$-dimensional singular harmonic oscillator and singular Coulomb potentials

Bound-state solutions of the singular harmonic oscillator and singular Coulomb potentials in arbitrary dimensions are generated in a simple way from the solutions of the one-dimensional generalized Morse potential. The nonsingular harmonic oscillator and nonsingular Coulomb potentials in arbitrary dimensions with their additional accidental degeneracies are obtained as particular cases. Added bonuses from these mappings are the straightforward determination of the critical attractive singular potential, the proper boundary condition on the radial eigenfunction at the origin and the inexistence of bound states in a pure inversely quadratic potential.

quant-ph↗
arXiv2015

Revisiting the quantum harmonic oscillator via unilateral Fourier transforms

The literature on the exponential Fourier approach to the one-dimensional quantum harmonic oscillator problem is revised and criticized. It is shown that the solution of this problem has been built on faulty premises. The problem is revisited via the Fourier sine and cosine transform method and the stationary states are properly determined by requiring definite parity and square-integrable eigenfunctions.

quant-ph↗
arXiv2015

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

The problem of fermions in 1+1 dimensions in the presence of a pseudoscalar Coulomb potential plus a mixing of vector and scalar Coulomb potentials which have equal or opposite signs is investigated. We explore all the possible signs of the potentials and discuss their bound-state solutions for fermions and antifermions. We show the relation between spin and pseudospin symmetries by means of charge-conjugation and $γ^{5}$ chiral transformations. The cases of pure pseudoscalar and mixed vector-scalar potentials, already analyzed in previous works, are obtained as particular cases. The results presented can be extended to 3+1 dimensions.

hep-th↗
arXiv2014

Quasi-exactly-solvable confining solutions for spin-1 and spin-0 bosons in (1+1)-dimensions with a scalar linear potential

We point out a misleading treatment in the recent literature regarding confining solutions for a scalar potential in the context of the Duffin-Kemmer-Petiau theory. We further present the proper bound-state solutions in terms of the generalized Laguerre polynomials and show that the eigenvalues and eigenfunctions depend on the solutions of algebraic equations involving the potential parameter and the quantum number.

quant-ph↗
arXiv2014

The simplest example of the use of the method of images

It is shown that the system consisting of two infinite and parallel planes, one of them a conductor, and the other an insulator with a uniform distribution of charges, is the simplest example of the use of the method of images, in contrast to what is diffused in the literature.

physics.class-ph↗
arXiv2013

A brief discussion on the possible bound states for a class of singular potentials

The one-dimensional Schrödinger equation for a class of potentials $V(|x|)$ which vanish at infinity and present dominant singularity at the origin in the form $α/|x|^β$ ($0<β\leq 2$) is investigated. The Hermiticity of the operators related to observable physical quantities is used to determinate the proper boundary conditions. Double degeneracy and exclusion of symmetric solutions, consonant the value of $β$, are discussed. Explicit solutions for the hydrogen atom and the Kratzer potential are presented.

quant-ph↗
arXiv2013

The singular harmonic oscillator revisited

The one-dimensional Schrödinger equation with the singular harmonic oscillator is investigated. The Hermiticity of the operators related to observable physical quantities is used as a criterion to show that the attractive or repulsive singular oscillator exhibits an infinite number of acceptable solutions provided the parameter responsible for the singularity is greater than a certain critical value, in disagreement with the literature. The problem for the whole line exhibits a two-fold degeneracy in the case of the singular oscillator, and the intrusion of additional solutions in the case of a nonsingular oscillator. Additionally, it is shown that the solution of the singular oscillator can not be obtained from the nonsingular oscillator via perturbation theory.

quant-ph↗
arXiv2008

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, $V_{v}+V_{s}= \mathrm{constant}$. These intrinsically relativistic and isospectral problems are solved in a 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.

hep-th↗
arXiv2007

Stationary states of spinless particles in square potentials

The one-dimensional Klein-Gordon equation is investigated with the most general Lorentz structure for the external potentials. The analysis and calculation of the reflection and transmission coefficients for the scattering of particles in a square potential, with an arbitrary mixing of vector and scalar couplings, reveal circumstances which conflict with the predictions from nonrelativistic quantum mechanics. It is shown that such anomalous scatterings are mediated by antiparticle bound states, even if the incident particles have low energies. The analysis of bound states also reveals surprising results, remarkable is the inhibition of the Schiff-Snyder-Weinberg effect due to the presence of a scalar coupling.

quant-ph↗