Related papers: Non-Central Potentials and Spherical Harmonics Usi…
I examine quantum mechanical Hamiltonians with partial supersymmetry, and explore two main applications. First, I analyze a theory with a logarithmic spectrum, and show how to use partial supersymmetry to reveal the underlying structure of…
In this work we present an introduction to Supersymmetry in the context of 1-dimensional Quantum Mechanics. For that purpose we develop the concept of hamiltonians factorization using the simple harmonic oscillator as an example, we…
Within the context of Supersymmetric Quantum Mechanics and its related hierarchies of integrable quantum Hamiltonians and potentials, a general programme is outlined and applied to its first two simplest illustrations. Going beyond the…
We propose an N=4 supersymmetric quantum mechanics of a charged particle on a sphere in the background of Dirac magnetic monopole and study the system using the CP(1) model approach. We explicitly calculate the symmetry algebra taking the…
The application of the hyperspherical harmonic approach to the case of non-local two-body potentials is described. Given the properties of the hyperspherical harmonic functions, there are no difficulties in considering the approach in both…
In this paper we study several aspects of extremal spherical symmetric black hole solutions of four dimensional N=1 supergravity coupled to vector and chiral multiplets with the scalar potential turned on. In the asymptotic region the…
We study the spherical quantum pseudodots in the Schrodinger equation using the pseudo-harmonic plus harmonic oscillator potentials considering the effect of the external electric and magnetic fields. The finite energy levels and the wave…
The Killingbeck potential consisting of the harmonic oscillator-plus-Cornell potential, is of great interest in high energy physics. The solution of Dirac equation with the Killingbeck potential is studied in the presence of the pseudospin…
A simple methodology is suggested for the efficient calculation of certain central potentials having singularities. The generalized pseudospectral method used in this work facilitates {\em nonuniform} and optimal spatial discretization.…
The perturbation method in supersymmetric quantum mechanics (SUSYQM) is used to study the spheroidal wave functions' recurrence relations, which are revealed by the shape-invariance property of the super-potential. The super-potential is…
The pseudoharmonic oscillator potential is studied in non relativistic quantum mechanics with a generalized uncertainty principle characterized by the existence of a minimal length scale. By using a perturbative approach, we analytically…
In this paper, a nice theoretical scheme is presented to investigate resonant and bound states in weakly bound nuclear systems by the use of isospectral potentials together with hyperspherical harmonics expansion. In this scheme, a new…
The supersymmetric analysis of spinning cosmic string spacetime, involving an electron in magnetic fields, has been conducted. We examined the Dirac system within extended special functions known as exceptional orthogonal polynomials.…
We describe the bound state and scattering properties of a quantum mechanical particle in a scalar $N$-prong potential. Such a study is of special interest since these situations are intermediate between one and two dimensions. The energy…
For any central potential V in D dimensions, the angular Schroedinger equation remains the same and defines the so called hyperspherical harmonics. For non-central models, the situation is more complicated. We contemplate two examples in…
We study the spectrum of spherically symmetric Dirac operators in three-dimensional space with potentials tending to infinity at infinity under weak regularity assumptions. We prove that purely absolutely continuous spectrum covers the…
Bound states of hyperbolic potential is investigated by means of a generalized pseudospectral method. Significantly improved eigenvalues, eigenfunctions are obtained efficiently for arbitrary $n, \ell$ quantum states by solving the relevant…
Supersymmetry allows one to build a hierarchy of Hamiltonians that share the same spectral properties and which are pairwise connected through common superpotentials. The iso-spectral properties of these Hamiltonians imply that the dynamics…
A new exact analytically solvable Eckart-type potential is presented, a generalisation of the Hulthen potential. The study through Supersymmetric Quantum Mechanics is presented together with the hierarchy of Hamiltonians and the shape…
In this paper we address again the issue of the scale anomaly in quantum mechanical models with inverse square potential. In particular we examine the interplay between the classical and quantum aspects of the system using in both cases an…