Related papers: Harmonic oscillators in a Snyder geometry
The geometric potential in quantum mechanics has been attracted attention recently, providing a formalism to investigate the influence of curvature in the context of low-dimensional systems. In this paper, we study the consequences of a…
A complete variational treatment is provided for a family of spiked-harmonic oscillator Hamiltonians H = -d^2/dx^2 + B x^2 + lambda/x^alpha, B > 0, lambda > 0, for arbitrary alpha > 0. A compact topological proof is presented that the set S…
In this paper we construct the coherent and trajectory-coherent states of a damped harmonic oscillator. We investigate the properties of this states.
We observe and analyze d-wave resonant scattering of bosons in tightly confining harmonic waveguides. It is shown that the d-wave resonance emerges in the quasi-1D regime as an imprint of a 3D d-wave shape resonance. A scaling relation for…
Spherical confinement in 3D harmonic, quartic and other higher oscillators of even order is studied. The generalized pseudospectral method is employed for accurate solution of relevant Schr\"odinger equation in an \emph{optimum,…
A variational and perturbative treatment is provided for a family of generalized spiked harmonic oscillator Hamiltonians H = -(d/dx)^2 + B x^2 + A/x^2 + lambda/x^alpha, where B > 0, A >= 0, and alpha and lambda denote two real positive…
For the displaced harmonic double-well oscillator the existence of exact polynomial bound states at certain displacements $d\,$ is revealed. The $N-$plets of these quasi-exactly solvable (QES) states are constructed in closed form. For…
The factorization method of Infeld and Hull is applied to the radial Schr\"{o}dinger equation for $d$-dimensional isotropic harmonic oscillator and various ladder operators are defined. The radial energy eigenstates are expressed in terms…
We analyse the properties of a strongly-damped quantum harmonic oscillator by means of an exact diagonalisation of the full Hamiltonian, including both the oscillator and the reservoir degrees of freedom to which it is coupled. Many of the…
Allowing for the inclusion of the parity operator, it is possible to construct an oscillator model whose Hamiltonian admits an EXACT square root, which is different from the conventional approach based on creation and annihilation…
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…
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…
By applying methods already discussed in a previous series of papers by the same authors, we construct here classes of integrable quantum systems which correspond to n fully resonant oscillators with nonlinear couplings. The same methods…
In the case of a one-dimensional nonsingular Hamiltonian $H$ and a singular supersymmetric partner $H_a$, the Darboux and factorization relations of supersymmetric quantum mechanics can be only formal relations. It was shown how we can…
The general version of the bosonic harmonic oscillator realisation of bosonic q-oscillators is given. It is shown that the currently known realisation is a special case of our general solution. The investigation has been performed at the…
Numerical evidence is given that spherically symmetric perturbations of stable spherically symmetric steady states of the gravitational Vlasov-Poisson system lead to solutions which oscillate in time. The oscillations can be periodic in…
A set of coupled complex Ginzburg-landau type amplitude equations which operates near a Hopf-Turing instability boundary is analytically investigated to show localized oscillatory patterns. The spatial structure of those patterns are the…
A family of relativistic geometric models is defined as a generalization of the actual anti-de Sitter (1+1) model of the relativistic harmonic oscillator. It is shown that all these models lead to the usual harmonic oscillator in the…
We study the isotropic and anisotropic Hamiltonian of two coupled harmonic oscillators from an algebraic approach of the $SU(1,1)$ and $SU(2)$ groups. In order to obtain the energy spectrum and eigenfunctions of this problem, we write its…
We study a class of quantum two-dimensional models with complex potentials of specific form. They can be considered as the generalization of a recently studied model with quadratic interaction not amenable to conventional separation of…