On the Klein–Gordon oscillator subject to a Coulomb-type potential

By introducing the scalar potential as modification in the mass term of the Klein–Gordon equation, the influence of a Coulomb-type potential on the Klein–Gordon oscillator is investigated. Relativistic bound states solutions are achieved to both attractive and repulsive Coulomb-type potentials and the arising of a quantum effect characterized by the dependence of angular frequency of the Klein–Gordon oscillator on the quantum numbers of the system is shown.     

An angular frequency dependence on the Aharonov–Casher geometric phase

A quantum effect characterized by a dependence of the angular frequency associated with the confinement of a neutral particle to a quantum ring on the quantum numbers of the system and the Aharonov–Casher geometric phase is discussed. Then, it is shown that persistent spin currents can arise in a two-dimensional quantum ring in the presence of a Coulomb-type potential. A particular contribution to the persistent spin currents arises from the dependence of the angular frequency on the geometric quantum phase.     

On the effects on a Landau-type system for an atom with no permanent electric dipole moment due to a Coulomb-type potential

We analyse the bound states for a Landau-type system for an atom with no permanent electric dipole moment subject to a Coulomb-type potential. By comparing the energy levels for bound states of the system with the Landau quantization for an atom with no permanent electric dipole moment (Furtado et al., 2006), we show that the energy levels of the Landau-type system are modified, where the degeneracy of the energy levels is broken. Another quantum effect investigated is a dependence of the angular frequency of the system on the quantum numbers associated with the radial modes and the angular momentum. As examples, we obtain the angular frequency and the energy levels associated with the ground state and the first excited state of the system.     

On a relation of the angular frequency to the Aharonov–Casher geometric phase in a quantum dot

By analysing the behaviour of a neutral particle with permanent magnetic dipole moment confined to a quantum dot in the presence of a radial electric field, Coulomb-type and linear confining potentials, then, an Aharonov–Bohm-type effect for bound states and a dependence of the angular frequency of the system on the Aharonov–Casher geometric phase and the quantum numbers associated with the radial modes, the angular momentum and the spin are obtained. In particular, the possible values of the angular frequency and the persistent spin currents associated with the ground state are investigated in two different cases.     

On a relativistic scalar particle subject to a Coulomb-type potential given by Lorentz symmetry breaking effects

The behaviour of a relativistic scalar particle in a possible scenario that arises from the violation of the Lorentz symmetry is investigated. The background of the Lorentz symmetry violation is defined by a tensor field that governs the Lorentz symmetry violation out of the Standard Model Extension. Thereby, we show that a Coulomb-type potential can be induced by Lorentz symmetry breaking effects and bound states solutions to the Klein–Gordon equation can be obtained. Further, we discuss the effects of this Coulomb-type potential on the confinement of the relativistic scalar particle to a linear confining potential by showing that bound states solutions to the Klein–Gordon equation can also be achieved, and obtain a quantum effect characterized by the dependence of a parameter of the linear confining potential on the quantum numbers {n,l}$\{n,l\}$ of the system.     

Aharonov-Bohm and non-inertial effects on a Klein-Gordon oscillator with potential in the cosmic string space-time with a spacelike dislocation

In this paper, we investigate the analogue effect to the Aharonov-Bohm effect for bound states in a relativistic quantum system described by the Klein-Gordon oscillator in the cosmic string space-time with a spacelike dislocation. We assume the topological defects have an internal magnetic flux and then analyze the effect on the relativistic energy eigenvalue subject to a Cornell-type potential and subsequently with a Coulomb-type potential. We show the presence of various potential parameters, the torsion parameter as well the cosmic string modify the energy spectrum.     

On a relativistic particle and a relativistic position-dependent mass particle subject to the Klein–Gordon oscillator and the Coulomb potential

The relativistic quantum dynamics of an electrically charged particle subject to the Klein–Gordon oscillator and the Coulomb potential is investigated. By searching for relativistic bound states, a particular quantum effect can be observed: a dependence of the angular frequency of the Klein–Gordon oscillator on the quantum numbers of the system. The meaning of this behaviour of the angular frequency is that only some specific values of the angular frequency of the Klein–Gordon oscillator are permitted in order to obtain bound state solutions. As an example, we obtain both the angular frequency and the energy level associated with the ground state of the relativistic system. Further, we analyse the behaviour of a relativistic position-dependent mass particle subject to the Klein–Gordon oscillator and the Coulomb potential.     

Aharonov-Casher effect and persistent spin currents in a Coulomb-type potential induced by Lorentz symmetry breaking effects

We investigate quantum effects on a nonrelativistic neutral particle with a permanent magnetic dipole moment that interacts with an electric field. This neutral particle is also under the influence of a background that breaks the Lorentz symmetry. We focus on the Lorentz symmetry violation background determined by a space-like vector field. Then, we show that the effects of the violation of Lorentz symmetry can yield an attractive Coulomb-type potential. Furthermore, we obtain the bound state solutions to the Schrödinger-Pauli equation and show that the spectrum of energy is a function of the Aharonov-Casher geometric quantum phase. Finally, we discuss the arising of persistent spin currents.     

Doubly uniform semiclassical quantization formula for resonances

The radial Schrödinger equation with an effective potential containing a single well and a single barrier is treated with an improved uniform semiclassical method. The improved quantization formula for complex energies (or resonances) contains a correction term that originates from a uniform treatment of the classically forbidden region near the origin in addition to the more familiar uniform treatment of the barrier region. In the present case the origin has a second-order pole, due to the centrifugal barrier potential term, and/or a Coulomb-type singularity, and these terms dominate the region inside the innermost classical turning point.Numerical results for first-order and third-order approximate complex resonance energies are compared with those of a standard (first- and third-order) barrier-uniform semiclassical method and also with those of ‘exact’ numerical computations.The improved quantization formula provides results in significantly better agreement with the exact results as the angular momentum quantum number l approaches zero.     

Aharonov–Bohm effect for bound states on spin-0 massive charged particles in a Gödel-type space–time with Coulomb potential

In this paper, we investigate the relativistic quantum dynamics of spin-0 massive charged particles in a Gödel-type space–time with electromagnetic interactions. We derive the radial wave equation of the Klein–Gordon equation with an internal magnetic flux field and Coulomb-type potential in the Som–Raychaudhuri space–time with cosmic string. We solve this equation and analyze the analog effect in relation to the Aharonov–Bohm effect for bound states.