Related papers: Algebraic discrete quantum harmonic oscillator wit…
This paper presents the first-order supersymmetric rational extension of the quantum anisotropic harmonic oscillator (QAHO) in multiple dimensions, including full-line, half-line, and their combinations. The exact solutions are in terms of…
We present a comprehensive study of the rational extension of the quantum anisotropic harmonic oscillator (QAHO) potentials with linear and/or quadratic perturbations. For the one-dimensional harmonic oscillator plus imaginary linear…
The classical and the quantal problem of a particle interacting in one-dimension with an external time-dependent quadratic potential and a constant inverse square potential is studied from the Lie-algebraic point of view. The integrability…
We present a simple algebraic procedure that can be applied to solve a range of quantum eigenvalue problems without the need to know the solution of the Schr\"odinger equation. The procedure, presented with a pedagogical purpose, is based…
Building upon our recently established correspondence between quantum cosmology and the hydrogen atom [1], we investigate the specific sector of a negative cosmological constant ($\Lambda < 0$) in a flat FLRW universe with dust. While the…
Using algebraic tools of supersymmetric quantum mechanics we construct classes of conditionally exactly solvable potentials being the supersymmetric partners of the linear or radial harmonic oscillator. With the help of the raising and…
The derivation of spherical harmonics is the same in nearly every quantum mechanics textbook and classroom. It is found to be difficult to follow, hard to understand, and challenging to reproduce by most students. In this work, we show how…
While the usual harmonic oscillator potential gives discrete energies in the non-relativistic case, it does not however give genuine bound states in the relativistic case if the potential is treated in the usual way. In the present article,…
We carry out a model-theoretic analysis of the Heisenberg algebra. To this end, a geometric structure is associated to the Heisenberg algebra and is shown to be a Zariski geometry. Furthermore, this Zariski geometry is shown to be…
We discuss various continuous and discrete symmetries of the supersymmetric simple harmonic oscillator (SHO) in one (0 + 1)-dimension of spacetime and show their relevance in the context of mathematics of differential geometry. We show the…
While quantum computing algorithms have been widely applied for electronic structure calculations, applications to molecular dynamics remain scarce. Complex and varied landscapes of molecular potential energy surfaces give rise to…
The generalized pseudospectral method is employed for the accurate calculation of eigenvalues, densities and expectation values for the spiked harmonic oscillators. This allows \emph{nonuniform} and \emph{optimal} spatial discretization of…
We construct a three-dimensional superconformal quantum mechanics (and its associated de Alfaro-Fubini-Furlan deformed oscillator) possessing an $sl(2|1)$ dynamical symmetry. At a coupling parameter $\beta\neq 0$ the Hamiltonian contains a…
The purely algebraic technique associated with the creation and annihilation operators to resolve the radial equation of Hydrogen-like atoms (HLA) for generating the bound energy spectrum and the corresponding wave functions is suitable for…
The double-scaling limit of the SYK (DSSYK) model is known to possess an underlying $\mathcal{U}_q(\mathfrak{su}(1,1))$ quantum group symmetry. In this paper, we provide, for the first time, a von Neumann algebraic quantum group-theoretical…
The spherical-harmonics expansion is a mathematically rigorous procedure and a powerful tool for the representation of potential energy surfaces of interacting molecular systems, determining their spectroscopic and dynamical properties,…
A simple discrete model of the two dimensional isotropic harmonic oscillator is presented. It is superintegrable with su(2) as its symmetry algebra. It is constructed with the help of the algebraic properties of the bivariate Charlier…
We study the radial part of the Dunkl-Coulomb problem in two dimensions and show that this problem possesses the $su(1,1)$ symmetry. We introduce two different realizations for the $su(1,1)$ Lie algebra and use the theory of irreducible…
The eigenstates of a real or complex cubic anharmonic oscillator are investigated using original and alternative methods. The procedure consists of determining global solutions of the Schr\"odinger equation that comply with the pertinent…
We study the canonical quantization of the damped harmonic oscillator by resorting to the realization of the q-deformation of the Weyl-Heisenberg algebra (q-WH) in terms of finite difference operators. We relate the damped oscillator…