Related papers: Quantum oscillator as 1D anyon
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 full spectrum and eigenfunctions of the quantum version of a nonlinear oscillator defined on an N-dimensional space with nonconstant curvature are rigorously found. Since the underlying curved space generates a position-dependent…
We present a mathematically rigorous quantum-mechanical treatment of a two-dimensional nonrelativistic quantum dual theories (with oscillator and Coulomb like potentials) on a plane and compare their spectra and the sets of eigenfunctions.…
A mapping is obtained relating radial screened Coulomb systems with low screening parameters to radial anharmonic oscillators in N-dimensional space. Using the formalism of supersymmetric quantum mechanics, it is shown that exact solutions…
Atomic-like systems in which electronic motion is two dimensional are now realizable as ``quantum dots''. In place of the attraction of a nucleus there is a confining potential, usually assumed to be quadratic. Additionally, a perpendicular…
We consider two-dimensional harmonic oscillator in the complex Bargmann-Fock-Segal representation with $T^*{\mathbb R}^{2}={\mathbb C}^2$ as classical phase space. We show that the eigenfunctions $\psi_n$ of the quantum Hamiltonian…
In this work we discuss about the problem of an electrically charged particle placed on the symmetry axis of an electrically charged ring in a quantum viewpoint. This problem should be an expanded version of the usual quantum ring and…
We establish a simple algebraic relationship between the energy eigenstates of the rational Calogero-Sutherland model with harmonic oscillator and Coulomb-like potentials. We show that there is an underlying SU(1,1) algebra in both of these…
A nonpolynomial one-dimensional quantum potential representing an oscillator, that can be considered as placed in the middle between the harmonic oscillator and the isotonic oscillator (harmonic oscillator with a centripetal barrier), is…
A linear quantum harmonic oscillator factors into one dimensional oscillators and can be solved using creation and annihilation operators. We consider a spherical analogue. This analogue does not factor. The two dimensional case is…
A nonlinear model of the quantum harmonic oscillator on two-dimensional spaces of constant curvature is exactly solved. This model depends of a parameter $\la$ that is related with the curvature of the space. Firstly the relation with other…
A similarity transformation is constructed through which a system of particles interacting with inverse-square two-body and harmonic potentials in one dimension, can be mapped identically, to a set of free harmonic oscillators. This…
Isotropic oscillator and Coulomb problems are known to have interesting correspondence. We focus on 2D quantum problems and present complete treatment on the correspondence including the Schroedinger equation, eigenfunctions and…
Energy-parity has been introduced by Kaplan and Sundrum as a protective symmetry that suppresses matter contributions to the cosmological constant [KS05]. It is shown here that this symmetry, schematically Energy --> - Energy, arises in the…
We give a technique for calculating the occupation number of quantum fields in time-dependent backgrounds by using the relation between one-dimensional {\em quantum} oscillators and two-dimensional {\em classical} oscillators. We illustrate…
Quantum simulation provides quantum systems under study with analogous controllable quantum systems and has wide applications from condensed-matter physics to high energy physics and to cosmology. The quantum system of a homogeneous and…
In this note we establish a relation between two exactly-solvable problems on circle, namely singular Coulomb and singular oscillator systems.
We consider a set of N linearly coupled harmonic oscillators and show that the diagonalization of this problem can be put in geometrical terms. The matrix techniques developed here allowed for solutions in both the classical and quantum…
We study a quantum spherically symmetric object which is based on radial plasma oscillations. Such a plasmoid is supposed to exist in a dense plasma containing electrons, ions, and neutral particles. The method of creation and annihilation…
Quantum entanglement has been actively sought for in optomechanical and electromechanical systems. The simplest such system is a mechanical oscillator interacting with a coherent beam, while the oscillator also suffers from thermal…