Related papers: Wigner quantum oscillators. Osp(3/2) oscillators
We generalized the squeeze and displacement operators of the one-dimensional harmonic oscillator to the three-dimensional case and based on these operators we construct the corresponding coherent and squeezed states. We have also calculated…
Some of the most enduring questions in physics--including the quantum measurement problem and the quantization of gravity--involve the interaction of a quantum system with a classical environment. Two linearly coupled harmonic oscillators…
A relativistic quantum harmonic oscillator in 3+1 dimensions is derived from a quaternionic non-relativistic quantum harmonic oscillator. This quaternionic equation also yields the Klein-Gordon wave equation with a covariant (space-time…
We investigate quantum properties of light in optical parametric oscillators (OPOs) based on four-wave mixing gain in media with third-order non-linearities. In spite of other competing $\chi^{(3)}$ effects, such as phase modulation,…
We introduce new representations to formulate quantum mechanics on noncommutative phase space, in which both coordinate-coordinate and momentum-momentum are noncommutative. These representations explicitly display entanglement properties…
We considered a two dimensional three electron quantum dot in a magnetic field in the Wigner limit. A unitary coordinate transformation decouples the Hamiltonian (with Coulomb interaction between the electrons included) into a sum of three…
The properties of a nonlinear oscillator with an additional term $k_g/x^2$, characterizing the isotonic oscillator, are studied. The nonlinearity affects to both the kinetic term and the potential and combines two nonlinearities associated…
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…
Quasiclassical solution of the three-dimensional Schredinger's equation is given. The existence of nonzero minimal angular momentum M_0 = \hbar /2 is shown, which corresponds to the quantum fluctuations of the angular momentum and…
The synchronization properties of two self-sustained quantum oscillators are studied in the Wigner representation. Instead of considering the quantum limit of the quantum van-der-Pol master equation we derive the quantum master equation…
New time dependent Wigner functions for the quantum harmonic oscillator have been obtained in this work. The Moyal equation for the harmonic oscillator has been presented as the wave equation of a 2D membrane in the phase plane. The values…
In this paper we study a model of the two-dimensional quantum harmonic oscillator in a 3-dimensional anti-de Sitter background. We use a generalized Schr\"odinger picture in which the analogs of the Schr\"odinger operators of the particle…
This work addresses the study of the oscillator algebra, defined by four parameters $p$, $q$, $\alpha$, and $\nu$. The time-independent Schr\"{o}dinger equation for the induced deformed harmonic oscillator is solved; explicit analytic…
The Bargmann-Wigner formalism is adapted to spherical surfaces embedded in three to eleven dimensions. This is demonstrated to generate wave equations in spherical space for a variety of antisymmetric tensor fields. Some of these equations…
A family of geometric models of quantum relativistic rotating oscillator is defined by using a set of one-parameter deformations of the static (3+1) de Sitter or anti-de Sitter metrics. It is shown that all these models lead to the usual…
We discuss a classical nonlinear oscillator, which is proved to be a superintegrable system for which the bounded motions are quasiperiodic oscillations and the unbounded (scattering) motions are represented by hyperbolic functions. This…
Despite conventional wisdom that spin-1/2 systems have no classical analog, we introduce a set of classical coupled oscillators with solutions that exactly map onto the dynamics of an unmeasured electron spin state in an arbitrary,…
The main characteristics of the quantum oscillator coherent states including the two-particle Calogero interaction are investigated. We show that these Calogero coherent states are the eigenstates of the second-order differential…
Under the spin-position decoupling approximation, a vector with a phase in 3D orientation space endowed with geometric algebra, substitutes the vector-matrix spin model built on the Pauli spin operator. The standard quantum operator-state…
The notion of f-oscillators generalizing q-oscillators is introduced. For classical and quantum cases, an interpretation of the f-oscillator is provided as corresponding to a special nonlinearity of vibration for which the frequency of…