Analytic solutions to the problem of Coulomb and confining potentials

M. Dineykhan, R. G. Nazmitdinov

备注：: 25 pages (Latex)
发表信息：: Phys.Atom.Nucl. 62 (1999) 138-149; Yad.Fiz. 62 (1999) 143-154

英文摘要：

The oscillator representation method is presented and used to calculate the energy spectra for a superposition of Coulomb and power-law potentials and for Coulomb and Yukawa potentials. The method provides an efficient way to obtain analytic results for arbitrary values of the parameters specifying the above-type potentials. The calculated energies of the ground and excited states of the quantum systems in question are found to comply well with exact results.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Bound state energies and wave functions of spherical quantum dots in presence of a confining potential model

We obtain the exact energy spectra and corresponding wave functions of the radial Schrödinger equation (RSE) for any (n,l) state in the presence of a combination of psudoharmonic, Coulomb and linear confining potential terms using an exact analytical iteration method. The interaction potential model under consideration is Cornell-modified plus harmonic (CMpH) type which is a correction form to the harmonic, Coulomb and linear confining potential terms. It is used to investigates the energy of electron in spherical quantum dot and the heavy quarkonia (QQ-onia).

2011-10-03quant-ph

On an atom with a magnetic quadrupole moment subject to harmonic and linear confining potentials

The quantum dynamics of an atom with a magnetic quadrupole moment that interacts with an external field subject to a harmonic and a linear confining potentials is investigated. It is shown that the interaction between the magnetic quadrupole moment and an electric field gives rise to an analogue of the Coulomb potential and, by confining this atom to a harmonic and a linear confining potentials, a quantum effect characterized by the dependence of the angular frequency on the quantum numbers of the system is obtained. In particular, it is shown that the possible values of the angular frequency …

2016-01-27quant-ph

Dirac Equations with Confining Potentials

This paper is devoted to a study of relativistic eigenstates of Dirac particles which are simultaneously bound by a static Coulomb potential and added linear confining potentials. It has recently been shown that, despite the addition of radially symmetric, linear confining potentials, some specific bound-state energies surprisingly retain their exact Dirac--Coulomb values (in the sense of an "exact symmetry"). This observation raises pertinent questions as to the generality of the cancellation mechanism. A Foldy-Wouthuysen transformation is used to find the relevant nonrelativistic physical de…

2015-02-06physics.atom-phquant-ph

An alternative simple solution of the sextic anharmonic oscillator and perturbed Coulomb problems

Utilizing an appropriate ansatz to the wave function, we reproduce the exact bound-state solutions of the radial Schrodinger equation to various exactly solvable sextic anharmonic oscillator and confining perturbed Coulomb models in $D$-dimensions. We show that the perturbed Coulomb problem with eigenvalue $E$ can be transformed to a sextic anharmonic oscillator problem with eigenvalue E. We also check the explicit relevance of these two related problems in higher-space dimensions. It is shown that exact solutions of these potentials exist when their coupling parameters with $k=D+2\ell $ appea…

2007-02-26quant-ph

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 lin…

2015-06-01hep-thquant-ph

Temperature dependence of Coulomb oscillations in a few-layer two-dimensional WS2 quantum dot

Standard semiconductor fabrication techniques are used to fabricate a quantum dot (QD) made of WS2, where Coulomb oscillations were found. The full-width-at-half-maximum of the Coulomb peaks increases linearly with temperature while the height of the peaks remains almost independent of temperature, which is consistent with standard semiconductor QD theory. Unlike graphene etched QDs, where Coulomb peaks belonging to the same QD can have different temperature dependences, these results indicate the absence of the disordered confining potential. This difference in the potential-forming mechanism…

2015-10-13cond-mat.mes-hallquant-ph

更多相关论文收起更多论文

Bound states by a pseudoscalar Coulomb potential in 1+1 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 …

2003-09-20hep-thquant-ph

Radial Coulomb and Oscillator Systems in Arbitrary Dimensions

A mapping is obtained relating analytical radial Coulomb systems in any dimension greater than one to analytical radial oscillators in any dimension. This mapping, involving supersymmetry-based quantum-defect theory, is possible for dimensions unavailable to conventional mappings. Among the special cases is an injection from bound states of the three-dimensional radial Coulomb system into a three-dimensional radial isotropic oscillator where one of the two systems has an analytical quantum defect. The issue of mapping the continuum states is briefly considered.

1996-02-10quant-ph

Confining non-analytic exponential potential $V(x)= g^2\exp\,(2|x|)$ and its exact Bessel-function solvability

In a previous paper we have shown that Schrödinger equation with the non-analytic attractive exponential potential $V(x)= -g^2\exp (-|x|)$ is exactly solvable. It has finitely many discrete eigenstates described by the Bessel function of the first kind $J_ν(z)$ and the eigenvalues are specified by the positive zeros of $J_ν(g)$ and $J'_ν(g)$ as a function of the order $ν$ with fixed $g>0$. Now we show the corresponding results for the {\em confining\/} non-analytic exponential potential $V(x)= g^2\exp (2|x|)$. This has infinitely many discrete eigenstates described by the modified Bessel funct…

2016-11-12math-phmath.CAmath.MP

Trapping of Topological-Structural Defects in Coulomb Crystals

We study experimentally and theoretically structural defects which are formed during the transition from a laser cooled cloud to a Coulomb crystal, consisting of tens of ions in a linear radio frequency trap. We demonstrate the creation of predicted topological defects (`kinks') in purely two-dimensional crystals, and also find kinks which show novel dynamical features in a regime of parameters not considered before. The kinks are always observed at the centre of the trap, showing a large nonlinear localized excitation, and the probability of their occurrence surprisingly saturates at ~0.5. Si…

2013-05-28physics.atom-phquant-ph

Mathematical predominance of Dirichlet condition for the one-dimensional Coulomb potential

We restrict a quantum particle under a coulombian potential (i.e., the Schrödinger operator with inverse of the distance potential) to three dimensional tubes along the x-axis and diameter $\varepsilon$, and study the confining limit $\varepsilon\to0$. In the repulsive case we prove a strong resolvent convergence to a one-dimensional limit operator, which presents Dirichlet boundary condition at the origin. Due to the possibility of the falling of the particle in the center of force, in the attractive case we need to regularize the potential and also prove a norm resolvent convergence to the D…

2012-05-29math-phmath.MPquant-ph