Related papers: Quantum Limits for Harmonic Oscillator
A linear quantum harmonic oscillator factors into one dimensional oscillators and can be solved using creation and annihilation operators. We consider a spherical analogue. This analogue does not factor. The two dimensional case is…
The Wigner function is a quantum analogue of the classical joined distribution of position and momentum. As such is should be a good tool to study quantum-classical correspondence. In this paper, the classical limit of the Wigner function…
In this work we investigate which radial field configuration yields bound states for neutral particles showing non-zero magnetic and electric dipole moments. The main result is that, in contrast with previous works, the Landau analog levels…
The paper reports on a study of a harmonic oscillator (ho) in the twisted Moyal space, in a well defined matrix basis, generated by the vector fields…
The classical dynamical system possessing a quantum spectrum of energy and "quantum" behavior is suggested and investigated. The proposed model can be considered as a dynamical variant of the old quantum theory for harmonic oscillator in…
The measurement of a quantum system becomes itself a quantum-mechanical process once the apparatus is internalized. That shift of perspective may result in different physical predictions for a variety of reasons. We present a model…
The equilibrium properties of an open harmonic oscillator are considered in three steps: First the creation and destruction operators are generalized for open dynamics and the creation operator is used to construct coherent states. The…
We show how sub-Planck phase-space structures in the Wigner function can be used to achieve Heisenberg-limited sensitivity in weak force measurements. Nonclassical states of harmonic oscillators, consisting of superpositions of coherent…
A convenient way to calculate $N$-particle quantum partition functions is by confining the particles in a weak harmonic potential instead of using a finite box or periodic boundary conditions. There is, however, a slightly different…
We continue our previous application of supersymmetric quantum mechanical methods to eigenvalue problems in the context of some deformed canonical commutation relations leading to nonzero minimal uncertainties in position and/or momentum.…
In this paper we discuss mechanical systems with inequality constraints. We demonstrate how such constraints can be taken into account by proper modification of the action which describes the original unconstrained dynamics. To illustrate…
This work prolongs, using an operator method, the investigations started in our recent paper J. Math. Phys. 51., 102108 on the spectrum and states of the harmonic oscillator on twisted Moyal plane, where rather a Moyal-star-algebraic…
Quantum gravity theories predict a minimal length at the order of magnitude of the Planck length, under which the concepts of space and time lose every physical meaning. In quantum mechanics, the insurgence of such minimal length can be…
In a recent work we have proposed an original analytic expression for the partition function of the quartic oscillator. This partition function, which has a simple and compact form with {\it no adjustable parameters}, reproduces some key…
Assuming that a constant potential energy function has meaning for a dissipated harmonic oscillator, then an important issue is the time dependence of the turning points. Turning point studies demonstrate that the common model of external…
In this paper, the $d$-dimensional quantum harmonic oscillator with a pseudo-differential time quasi-periodic perturbation \begin{equation}\label{0} \text{i}\dot{\psi}=(-\Delta+V(x)+\epsilon W(\omega t,x,-\text{i}\nabla))\psi,\ \ \ \ \…
An interesting observation was reported by Corrigan-Sasaki that all the frequencies of small oscillations around equilibrium are " quantised" for Calogero and Sutherland (C-S) systems, typical integrable multi-particle dynamics. We present…
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…
A master equation for the deformed quantum harmonic oscillator interacting with a dissipative environment, in particular with a thermal bath, is derived in the microscopic model by using perturbation theory. The coefficients of the master…
In this paper we continue the study of spectral properties of the Dunkl harmonic oscillator in the context of a finite reflection group on $\mathbb{R}^d$ isomorphic to $\mathbb{Z}^d_2$. We prove that imaginary powers of this operator are…