Related papers: Remarks on quantization of Pais-Uhlenbeck oscillat…
Noncommutative oscillators are first-quantized through an abelian Drinfel'd twist deformation of a Hopf algebra and its action on a module. Several important and subtle issues making possible the quantization are solved. The spectrum of the…
We study geometric quantization of the harmonic oscillator in terms of a singular real polarization given by fibres of the energy momentum map.
We revisit the canonical quantization to assess the spectrum of the modified Emden equation $\ddot{x} + kx\dot{x} + \omega^2 x + \frac{k^2}{9}x^3 = 0$, which is an isochronous case of the Li\'enard-Kukles equation. While its classical…
Meixner oscillators have a ground state and an `energy' spectrum that is equally spaced; they are a two-parameter family of models that satisfy a Hamiltonian equation with a {\it difference} operator. Meixner oscillators include as limits…
The stability of higher-order time derivative theories using the polymer extension of quantum mechanics is studied. First, we focus on the well-known Pais-Uhlenbeck model and by casting the theory into the sum of two decoupled The…
We have constructed coherent states for the higher derivative Pais-Uhlenbeck Oscillator. In the process we have suggested a novel way to construct coherent states for the oscillator having only negative energy levels. These coherent states…
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…
We calculate the eigenvalues of some two-dimensional non-Hermitian Hamiltonians by means of a pseudospectral method and straightforward diagonalization of the Hamiltonian matrix in a suitable basis set. Both sets of results agree remarkably…
We find that, in presence of the Snyder geometry, the quantization of d isotropic harmonic oscillators can be solved exactly.
Exactly solvable $N$-dimensional model of the quantum isotropic singular oscillator in the relativistic configurational $\vec r_N$-space is proposed. It is shown that through the simple substitutions the finite-difference equation for the…
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…
We consider the Euclidean path integral approach to higher-derivative theories proposed by Hawking and Hertog (Phys. Rev. D65 (2002), 103515). The Pais-Uhlenbeck oscillator is studied in some detail. The operator algebra is reconstructed…
We give a simple discussion of ghosts, unitarity violation, negative norm states and quantum vs classical behavior in the simplest model with four derivative action - the Pais-Uhlenbeck oscillator. We also point out that the normalizable…
An integrable anharmonic oscillator is presumably simulable by a classical computer and therefore by a quantum computer. An integrable anharmonic oscillator whose Hamiltonian is of normal type and quartic in the canonical coordinates is not…
In a recent paper a slightly modified version of the Bateman system, originally proposed to describe a damped harmonic oscillator, was proposed. This system is really different from the Bateman's one, in the sense that this latter cannot be…
In this paper we study the Hamiltonian structure of the second Painleve hierarchy, an infinite sequence of nonlinear ordinary differential equations containing PII as its simplest equation. The n-th element of the hierarchy is a non linear…
In the previous works \cite{N46,N47} authors have defined the oscillator-like system that associated with the two variable Chebyshev-Koornwinder polynomials. We call this system the generalized Chebyshev - Koornwinder oscillator. In this…
We study the generalized quantum isotonic oscillator Hamiltonian given by H=-d^2/dr^2+l(l+1)/r^2+w^2r^2+2g(r^2-a^2)/(r^2+a^2)^2, g>0. Two approaches are explored. A method for finding the quasi-polynomial solutions is presented, and…
We present a new exactly solvable (classical and quantum) model that can be interpreted as the generalization to the two-dimensional sphere and to the hyperbolic space of the two-dimensional anisotropic oscillator with any pair of…
In the harmonic oscillator representation, the Schrodinger equation has a form of a set of infinite number of algebraical equations which are labeled by the radial quantum number "n". It is shown that at n>>1 these equations are…