Related papers: Topological quantization of the harmonic oscillato…
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…
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…
We show how several important classical problems, with positive definite potential energy, can be solved by starting from the factorization of the total mechanical energy using complex numbers. In particular, we derive in a new way exact…
We theoretically propose how to observe topological effects in a generic classical system of coupled harmonic oscillators, such as classical pendula or lumped-element electric circuits, whose oscillation frequency is modulated fast in time.…
The 1-D dimension harmonic oscillator in Snyder space is investigated in its classical and quantum versions. The classical trajectory is obtained and the semiclassical quantization from the phase space trajectories is discussed. In the…
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…
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…
The q-deformed harmonic oscillator is studied in the light of q-deformed phase space variables. This allows a formulation of the corresponding Hamiltonian in terms of the ordinary canonical variables $x$ and $p$. The spectrum shows…
We study the semirelativistic Hamiltonian operator composed of the relativistic kinetic energy and a static harmonic-oscillator potential in three spatial dimensions and construct, for bound states with vanishing orbital angular momentum,…
The electronic bands are classified according to their topology. We compute the connection and curvature for the electronic bands and show that the physical properties are determined by topological invariants which are equivalent to the…
We revisit the quantum-mechanical two-dimensional harmonic oscillator with an electric field confined to a circular box of impenetrable walls. In order to obtain the energy spectrum we resort to the Rayleigh-Ritz method with polynomial and…
We settle affirmatively the isospectral problem for quantum toric integrable systems: the semiclassical joint spectrum of such a system, given by a sequence of commuting Toeplitz operators on a sequence of Hilbert spaces, determines the…
Classical physics is reformulated as a constrained Hamiltonian system in the history phase space. Dynamics, i.e. the Euler-Lagrange equations, play the role of first-class constraints. This allows us to apply standard methods from the…
By using the Feynman-Hibbs prescription for the evolution amplitude, we quantize the system of a damped harmonic oscillator coupled to its time-reversed image, known as Bateman's dual system. The time-dependent quantum states of such a…
We provide a new canonical approach for studying the quantum mechanical damped harmonic oscillator based on the doubling of degrees of freedom approach. Explicit expressions for Lagrangians of the elementary modes of the problem,…
In this paper, the Higgs-like approach is used to analyze the quantum dynamics of a harmonic oscillator constrained on a circle. We obtain the Hamiltonian of this system as a function of the Cartesian coordinate of the tangent line through…
We apply topological methods to obtain global continuation results for harmonic solutions of some periodically perturbed ordinary differential equations on a $k$-dimensional differentiable manifold $M \subseteq \mathbb{R}^m$. We assume that…
We investigate the quantization of a free particle coupled linearly to a harmonic oscillator. This system, whose classical counterpart has clearly separated regular and chaotic regions, provides an ideal framework for studying the…
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…
In the context of a two-parameter $(\alpha, \beta)$ deformation of the canonical commutation relation leading to nonzero minimal uncertainties in both position and momentum, the harmonic oscillator spectrum and eigenvectors are determined…