相关论文: Discrete-to-continuum transitions and mathematical…
Motivated by improving the understanding of the quantum-to-classical transition we use a simple model of classical discrete interactions for studying the discrete-to-continuous transition in the classical harmonic oscillator. A parallel is…
The dynamics of hybrid systems -- i.e. ones in which classical and quantum degrees of freedom co-exist and interact -- feature both diffusion in the classical sector and decoherence in the quantum state. In this article, we will consider…
We discuss the exact discretization of the classical harmonic oscillator equation (including the inhomogeneous case and multidimensional generalizations) with a special stress on the energy integral. We present and suggest some numerical…
A simple derivation of the classical solutions of a nonlinear model describing a harmonic oscillator on the sphere and the hyperbolic plane is presented in polar coordinates. These solutions are then related to those in cartesian…
The classical and quantum dynamics of the noncanonically coupled oscillators is considered. It is shown that though the classical dynamics is well--defined for both harmonic and anharmonic oscillators, the quantum one is well--defined in…
A classic harmonic oscillator model is developed to investigate the optical properties of coupled metal nanoparticles (MNPs) with arbitrary configuration in plane. The coupling coefficients are derived from classical electrodynamics. Using…
A certain notion of canonical equivalence in quantum mechanics is proposed. It is used to relate quantal systems with discrete ones. Discrete systems canonically equivalent to the celebrated harmonic oscillator as well as the quartic and…
In a previous paper a formalism to analyze the dynamical evolution of classical and quantum probability distributions in terms of their moments was presented. Here the application of this formalism to the system of a particle moving on a…
Revisiting canonical integration of the classical pendulum around its unstable equilibrium, normal hyperbolic canonical coordinates are constructed
Classical oscillator differential equation is replaced by the corresponding (finite time) difference equation. The equation is, then, symmetrized so that it remains invariant under the change d going to -d, where d is the smallest span of…
The standard quantum mechanical harmonic oscillator has an exact, dual relationship with a completely classical system: a classical particle running along a circle. Duality here means that there is a one-to-one relation between all…
Harmonic oscillator in Fock space is defined. Isospectral as well as polynomiality-of-eigenfunctions preserving, translation-invariant discretization of the harmonic oscillator is presented. Dilatation-invariant and…
The basic concepts of classical mechanics are given in the operator form. The dynamical equation for a hybrid system, consisting of quantum and classical subsystems, is introduced and analyzed in the case of an ideal nonselective…
The Darbroux transformation is generalized for time-dependent Hamiltonian systems which include a term linear in momentum and a time-dependent mass. The formalism for the $N$-fold application of the transformation is also established, and…
The Feynman path integral for the generalized harmonic oscillator is reviewed, and it is shown that the path integral can be used to find a complete set of wave functions for the oscillator. Harmonic oscillators with different…
A generalized harmonic oscillator on noncommutative spaces is considered. Dynamical symmetries and physical equivalence of noncommutative systems with the same energy spectrum are investigated and discussed. General solutions of…
We obtain a class of parametric oscillation modes that we call K-modes with damping and absorption that are connected to the classical harmonic oscillator modes through the "supersymmetric" one-dimensional matrix procedure similar to…
We describe quantum behaviors of a simple harmonic oscillator, starting from the classical mechanics. By imposing two conditions on the phase points generated from a symplectic algorithm, we obtain discrete energy levels, satisfying $E_n…
A generalization of classical mechanics is obtained from a complex parametrization of the phase space. The formalism supports complex Hamiltonian functions describing non-conservative classical mechanical systems. A quantization scheme that…
The Kravchuk and Meixner polynomials of discrete variable are introduced for the discrete models of the harmonic oscillator and hydrogen atom. Starting from Rodrigues formula we construct raising and lowering operators, commutation and…