Related papers: When q=0, The Forced Harmonic Oscillator Isn't
A generalization of the canonical coherent states of a quantum harmonic oscillator has been performed by requiring the conditions of normalizability, continuity in the label and resolution of the identity operator with a positive weight…
Though algorithms for quantum simulation of Quantum Harmonic Oscillator (QHO) have been proposed, still they have not yet been experimentally verified. Here, for the first time, we demonstrate a quantum simulation of QHO in the presence of…
Specific nonequilibrium states of the quantum harmonic oscillator described by the Lindblad equation have been hereby suggested. This equation makes it possible to determine time-varying effects produced by statistical operator or…
We study the canonical quantization of the damped harmonic oscillator by resorting to the realization of the q-deformation of the Weyl-Heisenberg algebra (q-WH) in terms of finite difference operators. We relate the damped oscillator…
In this work, previous results concerning the infinitely many zeros of single stochastic oscillators driven by random forces are extended to the general class of coupled stochastic oscillators. We focus on three main subjects: 1) the…
The finite q-oscillator is a model that obeys the dynamics of the harmonic oscillator, with the operators of position, momentum and Hamiltonian being functions of elements of the q-algebra su_q(2). The spectrum of position in this discrete…
By factorization of the Hamiltonian describing the quantum mechanics of the continuous q-Hermite polynomial, the creation and annihilation operators of the q-oscillator are obtained. They satisfy a q-oscillator algebra as a consequence of…
We revisit the quantized version of the harmonic oscillator obtained through a q-dependent family of coherent states. For each q, 0< q < 1, these normalized states form an overcomplete set that resolves the unity with respect to an explicit…
It is proven that the energy of a quantum mechanical harmonic oscillator with a generically time-dependent but cyclic frequency, $\omega_{0}(t_{0})= \omega_{0}(0)$, cannot decrease on the average if the system is originally in a stationary…
We address the problem of determining whether or not a harmonic oscillator has been perturbed by an external force. Quantum detection and estimation theory has been used in devising optimum measurement schemes. Detection probability has…
A harmonic oscillator with time-dependent mass $m(t)$ and a time-dependent (squared) frequency $\omega^2(t)$ occurs in the modelling of several physical systems. It is generally believed that systems, with $m(t)>0$ and $\omega^2(t)>0$…
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…
We extend the stochastic quantization method recently developed by Haba and Kleinert to non-autonomous mechanical systems, in the case of the time-dependent harmonic oscillator. In comparison with the autonomous case, the quantization…
Normally, the half-harmonic oscillator is active when $x>0$ and absent when $x<0$. From a canonical quantization perspective, this leads to odd eigenfunctions being present while even eigenfunctions are absent. In that case, only the usual…
Evolution of coherent states is considered for a particle confined to a cylinder moving in a harmonic oscillator potential. Because of the discontinuous changes as time goes by of the phase representing the position of a particle on a…
Geometrical formulation of classical mechanics with forces that are not necessarily potential-generated is presented. It is shown that a natural geometrical "playground" for a mechanical system of point particles lacking Lagrangian and/or…
A family of quantum anharmonic oscillators is studied in any finite spatial dimension in the scheme of first quantization and the investigation of their eigenenergies is presented. The statistical properties of the calculated eigenenergies…
A harmonic oscillator is an indefinite-frequency one if the parameter $\omega$ is replaced by an operator. An ensemble of $N$ such oscillators may be regarded as a toy model of a bosonic quantum field. All the possible frequencies…
The transformation of a classical system into its quantum counterpart is usually done through the well known procedure of canonical quantization. However, on non-Cartesian domains, or on bounded Cartesian domains, this procedure can be…
Problems concerning with application of quantum rules on classical phenomena have been widely studied, for which lifted up the idea about quantization and uncertainty principle. Energy quantization on classical example of simple harmonic…