Related papers: Condition for minimal Harmonic Oscillator Action
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…
In this work we explicitly solve the problem of the harmonic oscillator in the classical limit of a minimal-length scenario. We show that (i) the motion equation of the oscillator is not linear anymore because the presence of a minimal…
Minimising movements are investigated for an energy which is the superposition of a convex functional and fast small oscillations. Thus a minimising movement scheme involves a temporal parameter $\tau$ and a spatial parameter $\epsilon$,…
The pseudoharmonic oscillator potential is studied in non relativistic quantum mechanics with a generalized uncertainty principle characterized by the existence of a minimal length scale. By using a perturbative approach, we analytically…
The frequency of a classical periodic system can be obtained using action variables without solving the dynamical equations. We demonstrate the construction of two equivalent forms of the action variable for a one dimensional relativistic…
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…
In this paper, we investigate a two dimensional isotropic harmonic oscillator on a time-dependent spherical background. The effect of the background can be represented as a minimally coupled field to the oscillator's Hamiltonian. For a…
A system obeying the harmonic oscillator equation of motion can be used as a force or proper acceleration sensor. In this short review we derive analytical expressions for the sensitivity of such sensors in a range of different situations,…
We prove the reducibility of 1-D quantum harmonic oscillators in $\mathbb R$ perturbed by a quasi-periodic in time potential $V(x,\omega t)$ under the following conditions, namely there is a $C>0$ such that \begin{equation*}…
The Fourier series method is used to solve the homogeneous equation governing the motion of the harmonic oscillator. It is shown that the general solution to the problem can be found in a surprisingly simple way for the case of the simple…
We consider countable system of harmonic oscillators on the real line with quadratic interaction potential with finite support and local external force (stationary stochastic process) acting only on one fixed particle. In the case of…
Motivated by the experimental transport of a trap with a quantum mechanical system modeled as a harmonic oscillator (h.o.) the corresponding classical problem is investigated. Protocols for the fastest possible transport of a classical h.o.…
The minimal work principle asserts that work done on a thermally isolated equilibrium system, is minimal for the slowest (adiabatic) realization of a given process. This principle, one of the formulations of the second law, is operationally…
By controlling coefficients and decaying order of time-decaying harmonic potentials, the velocity of a quantum particle is decelerated by the effect of harmonic potentials but the particle is non-trapping. In this paper, we consider the…
We analyze the effect of having minimum length on a two dimensional anisotropic simple harmonic oscillator with PT symmetric imaginary interaction perturbatively. First order correction to the general state is calculated analytically to…
The quantization of a constant of motion for the harmonic oscillator with a time-explicitly depending external force is carried out. This quantization approach is compared with the normal Hamiltonian quantization approach. Numerical results…
Controlled time-decaying harmonic potentials decelerate the velocity of the charged particle but the particle never be trapped by this harmonic potentials. This physical phenomena changes threshold between the short range class of potential…
We consider a harmonic oscillator (HO) with a time dependent frequency which undergoes two successive abrupt changes. By assumption, the HO starts in its fundamental state with frequency \omega_{0}, then, at t = 0, its frequency suddenly…
We determine the energy eigenvalues and eigenfunctions of the harmonic oscillator where the coordinates and momenta are assumed to obey the modified commutation relations [x_i,p_j]=i hbar[(1+ beta p^2) delta_{ij} + beta' p_i p_j]. These…
The periodically driven harmonic oscillator with damping is one of the most elementary and trusted models in physics and normally applied in its steady state, disregarding specific initial conditions and associated transients. For example,…