Related papers: About dual two-dimensional oscillator and Coulomb-…
We present a mathematically rigorous quantum-mechanical treatment of a one-dimensional nonrelativistic quantum dual theories (with oscillator and Coulomb-like potentials) and compare their spectra and the sets of eigenfunctions. We…
We present a mathematically rigorous quantum-mechanical treatment of a two-dimensional nonrelativistic quantum dual theories (with oscillator and Coulomb like potentials) on pseudosphere and compare their spectra and the sets of…
The quantum-mechanical problems of a nonrelativistic free particle, a harmonic oscillator and a Coulomb particle on Minkowski plane are discussed. The Schr\"odinger equations for eigenvalues are obtained using the Beltrami-Laplas operator…
We extend the notion of Dirac oscillator in two dimensions, to construct a set of potentials. These potentials becomes exactly and quasi-exactly solvable potentials of non-relativistic quantum mechanics when they are transformed into a…
We present a mathematically rigorous quantum-mechanical treatment of a one-dimensional nonrelativistic motion of a particle in the potential field $V(x)=g_{1}x^{-1}+g_{2}x^{-2}$. For $g_{2}>0$ and $g_{1}<0$, the potential is known as the…
The effects on the non-relativistic dynamics of a system compound by two electrons interacting by a Coulomb potential and with an external harmonic oscillator potential, confined to move in a two dimensional Euclidean space, are…
It is shown that the Schrodinger equation for a large family of pairs of two-dimensional quantum potentials possess wavefuctions for which the amplitude and the phase are interchangeable, producing two different solutions which are dual to…
The Schr\"odinger equations for the Coulomb and the Harmonic oscillator potentials are solved in the cosmic-string conical space-time. The spherical harmonics with angular deficit are introduced. The algebraic construction of the harmonic…
In this paper we establish a relation between Coulomb and oscillator systems on $n$-dimensional spheres and hyperboloids for $n\geq 2$. We show that, as in Euclidean space, the quasiradial equation for the $n+1$ dimensional Coulomb problem…
The so-called 2d/4d correspondences connect two-dimensional conformal field theory (2d CFT), N=2 supersymmetric gauge theories and quantum integrable systems. The latter in the simplest case of the SU(2) gauge group are nothing but the…
Two planar supersymmetric quantum mechanical systems built around the quantum integrable Kepler/Coulomb and Euler/Coulomb problems are analyzed in depth. The supersymmetric spectra of both systems are unveiled, profiting from symmetry…
We study the quantum behaviour of a particle moving in a one-dimensional double well potential. This double well is obtained by gluing together, at the origin, two shifted harmonic oscillator potentials. The Schr\"odinger equation is…
In this paper, a quantum dot mathematical model based on a two-dimensional Schr\"odinger equation assuming the 1/r inter-electronic potential is revisited. Generally, it is argued that the solutions of this model obtained by solving a…
We present a new exactly solvable quantum problem for which the Schroedinger equation allows for separation of variables in oblate spheroidal coordinates. Namely, this is the quantum mechanical two Coulomb centers problem for the case of…
We investigate the existence of resonances for two-centers Coulomb systems with arbitrary charges in two dimensions, defining them in terms of generalised complex eigenvalues of a non-selfadjoint deformation of the two-centers Schr\"odinger…
This paper presents analytical solutions for eigenvalues and eigenfunctions of the Schr\"odinger equation in higher dimensions, incorporating the Dunkl operator. Two fundamental quantum mechanical problems are examined in their exact forms:…
We analyze two conditionally solvable quantum-mechanical models: a one-dimensional sextic oscillator and a perturbed Coulomb problem. Both lead to a three-term recurrence relation for the expansion coefficients. We show diagrams of the…
Based on the tensor method, a q-analoque of the spin-orbit coupling is introduced in a q-deformed Schroedinger equation, previously derived for a central potential. Analytic expressions for the matrix elemnets of the representation j=l\pm…
The time-dependent quantum system of two laser-driven electrons in a harmonic oscillator potential is analysed, taking into account the repulsive Coulomb interaction between both particles. The Schrodinger equation of the two-particle…
The model of a two-electron quantum dot, confined to move in a two dimensional flat space, is revisited. Generally, it is argued that the solutions of this model obtained by solving a biconfluent Heun equation have some limitations. In…