相关论文: Dynamical invariants and quantization of the one-d…
We show that, by using the quantum orthogonal functions invariant, we are able to solve a coupled of time dependent harmonic oscillators where all the time dependent frequencies are arbitrary. We do so, by transforming the time dependent…
In this paper we have obtained the exact eigenstates of a two dimensional damped harmonic oscillator in the presence of an external magnetic field varying with respect to time in time dependent noncommutative space. It has been observed…
A general dynamical invariant operator for three coupled time-dependent oscillators is derived. Although the obtained invariant operator satisfies the Liouville-von Neumann equation, its mathematical formula is somewhat complicated due to…
Quantum dynamical semigroups are applied to the study of the time evolution of harmonic oscillators, both bosonic and fermionic. Explicit expressions for the density matrices describing the states of these systems are derived using the…
We review some aspects of the quantization of the damped harmonic oscillator. We derive the exact action for a damped mechanical system in the frame of the path integral formulation of the quantum Brownian motion problem developed by…
In this manuscript, we investigate the analytical solution of the time-dependent Schr\"odinger equation for a harmonic oscillator with time-dependent mass and frequency, coupled with angular-dependent potential energy by utilizing the Dunkl…
An explicit solution of the equation for the classical harmonic oscillator with smooth switching of the frequency has been found . A detailed analysis of a quantum harmonic oscillator with such frequency has been done on the base of the…
Two-dimensional systems with time-dependent controls admit a quadratic Hamiltonian modelling near potential minima. Independent, dynamical normal modes facilitate inverse Hamiltonian engineering to control the system dynamics, but some…
In the Heisenberg picture, the generalized invariant and exact quantum motions are found for a time-dependent forced harmonic oscillator. We find the eigenstate and the coherent state of the invariant and show that the dispersions of these…
The dynamics of time-dependent coupled oscillator model for the charged particle motion subjected to a time-dependent external magnetic field is investigated. We used canonical transformation approach for the classical treatment of the…
We propose a scheme to deal with certain time-dependent non-Hermitian Hamiltonian operators $H(t)$ that generate a real phase in their time-evolution. This involves the use of invariant operators $I_{PH}(t)$ that are pseudo-Hermitian with…
A simple pseudo-Hamiltonian formulation is proposed for the linear inhomogeneous systems of ODEs. In contrast to the usual Hamiltonian mechanics, our approach is based on the use of non-stationary Poisson brackets, i.e. corresponding…
The center of mass motion of trapped ions and neutral atoms is suitable for approximation by a time-dependent driven quantum harmonic oscillator whose frequency and driving strength may be controlled with high precision. We show the time…
Based on a simple observation that a classical second order differential equation may be decomposed into a set of two first order equations, we introduce a Hamiltonian framework to quantize the damped systems. In particular, we analyze the…
The classical and quantum formalism for a p-adic and adelic harmonic oscillator with time-dependent frequency is developed, and general formulae for main theoretical quantities are obtained. In particular, the p-adic propagator is…
In this article, the problem of the charged harmonic plus an inverse harmonic oscillator with time-dependent mass and frequency in a time-dependent electromagnetic field is investigated. It is reduced to the problem of the inverse harmonic…
Classical and quantum mechanical analysis have been carried out on harmonic like oscillator with asymmetric position dependent mass. Phase space analysis are performed both classically and quantum mechanically for a plausible understanding…
The resonances associated with a fractional damped oscillator which is driven by an oscillatory external force are studied. It is shown that such resonances can be manipulated by tuning up either the coefficient of the fractional damping or…
New families of time-dependent potentials related to the parametric oscillator are introduced. This is achieved by introducing some general time-dependent operators that factorize the appropriate constant of motion (quantum invariant) of…
This paper explores a mathematical technique for deriving dynamical invariants (i.e. constants of motion) in time-dependent gravitational potentials. The method relies on the construction of a canonical transformation that removes the…