A Supersymmetric Treatment of a Particle Subjected to a Ring-shaped Potential

Supersymmetry and the Hartmann Potential of Theoretical Chemistry

The ring-shaped Hartmann potential $ V = ησ^{2} ε_{0} \left( \frac{2 a_{0}}{r} - \frac{ηa_{0}^{2}}{r^{2} sin^{2} θ} \right) $ was introduced in quantum chemistry to describe ring-shaped molecules like benzene. In this article, the supersymmetric features of the Hartmann potential are discussed. We first review the results of a previous paper in which we rederived the eigenvalues and radial eigenfunctions of the Hartmann potential using a formulation of one-dimensional supersymmetric quantum mechanics (SUSYQM) on the half-line $\left[ 0, \infty \right)$. A reformulation of SUSYQM in the full li…

Supersymmetric Quantum Mechanics and Solitons of the sine-Gordon and Nonlinear Schrödinger Equations

We present a case demonstrating the connection between supersymmetric quantum mechanics (SUSY--QM), reflectionless scattering, and soliton solutions of integrable partial differential equations. We show that the members of a class of reflectionless Hamiltonians, namely, Akulin's Hamiltonians, are connected via supersymmetric chains to a potential-free Hamiltonian, explaining their reflectionless nature. While the reflectionless property in question has been mentioned in the literature for over two decades, the enabling algebraic mechanism was previously unknown. Our results indicate that the m…

原子-场相互作用中的时间依赖空间纠缠

Time dependent spatial entanglement in atom-field interaction

本文利用时间依赖量子蒙特卡洛方法研究原子在超短激光脉冲下的空间纠缠，发现通过相位调制可操控纠缠，负啁啾增强而正啁啾抑制纠缠。

Bound State Solution of the Klein-Fock-Gordon equation with the Hulthén plus a Ring-Shaped like potential within SUSY quantum mechanics

In this paper, the bound state solution of the modified Klein-Fock-Gordon equation is obtained for the Hulthén plus ring-shaped lake potential by using the developed scheme to overcome the centrifugal part. The energy eigenvalues and corresponding radial and azimuthal wave functions are defined for any $l\neq0$ angular momentum case on the conditions that scalar potential is whether equal and nonequal to vector potential, the bound state solutions of the Klein-Fock-Gordon equation of the Hulthén plus ring-shaped like potential are obtained by Nikiforov-Uvarov (NU) and supersymmetric quantum me…

介观量子环中螺旋位错对三次谐波产生的拓扑控制

Topological control of third-harmonic generation in a mesoscopic quantum ring with spiral dislocation

研究螺旋位错介观量子环中的三次谐波产生，通过扭转诱导空间变形改变有效度规，结合径向约束和磁场求解束缚态，计算非线性极化率，证明螺旋位错可作为调控非线性光学活性的几何旋钮。