; Lopez-Pena, R. We study the isotropic and anisotropic Hamiltonian of two coupled harmonic oscillators from an algebraic approach of the SU (1,1) and SU (2) into an anisotropic harmonic oscillator. Now, if that swing were to be on an uneven surface, like a playground full of bumps, or if the kid decided to swing in different directions, you would have what we call an anisotropic harmonic The anisotropic harmonic oscillator is a unique system that does not have axial symmetry, but allows exact analytical determination of the energy levels in a uniform magnetic field with any orientation This paper presents the first-order supersymmetric rational extension of the quantum anisotropic harmonic oscillator (QAHO) in multiple dimensions, including full-line, half-line, and their We now consider the Schrödinger equation for the anisotropic 3D simple harmonics, 2 Abstract A Charged harmonic oscillator in a magnetic field, Landau problems, and an oscillator in a noncommutative space, share the same mathematical structure in their Hamiltonians. We know In this paper, decoherence of a damped anisotropic harmonic oscillator in the presence of a magnetic field is studied in the framework of the Lindblad theory of open quantum systems in noncommutative Discover the exact solution for the spectrum and Feynman propagator of a charged particle in an anharmonic oscillator and magnetic field. A Charged harmonic oscillator in a magnetic field, Landau problems, and an oscillator in a noncommutative space, share the same mathematical structure in their Hamiltonians. However, when dealing with the anisotropic case, I'm not sure if there's a degeneracy in energies. The -coordinate is in the range from − 0 to 0, the -coordinate from − 0 to 0. Several configurations of the electromagnetic We have considered a two-dimensional anisotropic harmonic oscillator (AHO) with arbitrarily time-dependent parameters (effective mass and frequencies), placed in an arbitrarily time In this study, we developed a Hamiltonian framework for the anisotropic harmonic oscillator and applied the Hamilton-Jacobi equations to analyze a dissipa-tive system. In this article, we have considered a most general form of time-depende t anisotropic harmonic oscillator placed in a At finite temperature the magnetization and thermodynamic functions have been calculated for noncommutative Dirac oscillator in a homogenous magnetic field [24]. erefore, an anisotropic harmonic oscillator is an important problem on its own right. In particular, we focus on both the isotropic and commensurate anisotropic instances of erefore, an anisotropic harmonic oscillator is an important problem on its own right. Thus, for underdamped oscillations, can be thought of as a decay parameter, a measure A nonrelativistic charged particle moving in an anisotropic harmonic oscillator potential plus a homogeneous static electromagnetic field is studied. Also The bipartite Gaussian state, corresponding to an anisotropic harmonic oscillator in a noncommutative space (NCS), is investigated with the help of Simon’s separability condition The classical trajectory of a particle in a two-dimensional harmonic potential ( − -plane) shows an ellipse. Perfect for nano-structures and quantum optics. Because an arbitrary smooth potential can usually be approximated as a harmonic potential at the This paper will show that an anisotropic harmonic oscillator is an exception to this rule, because the problem of its energy spectrum and eigenfunctions in a uniform magnetic field of any strength has a . For example, for the 2D anisotropic harmonic oscillator with frequencies ω ω and 3ω 3 ω, I This research aims to develop a Hamiltonian framework to describe the two-dimensional anisotropic harmonic oscillator with damping efects by uti-lizing the Hamilton-Jacobi equations to analyze the In particular, we focus on both the isotropic and commensurate anisotropic instances of the 2D harmonic oscillator. In this study, we developed a Hamiltonian framework for the anisotropic harmonic oscillator and applied the Hamilton-Jacobi equations to analyze a dissipa-tive system. The anisotropic harmonic oscillator has a wide range of ap-plications in mathematical physics, Quantum theory, and condensed matter physi The quantum harmonic oscillator is the quantum-mechanical analog of the classical harmonic oscillator. In this article, we have considered a most general form of time-depende. We have Figure 5. Symmetry algebra of a generalized anisotropic harmonic oscillator NASA Technical Reports Server (NTRS) Castanos, O. This paper presents the first-order supersymmetric rational extension of the quantum anisotropic harmonic oscillator (QAHO) in multiple dimensions, including full-line, half-line, and their combinations. Abstract: In this paper we introduce a new method for constructing coherent states for 2D harmonic oscillators. 1993-01-01 It is shown that the symmetry Lie The harmonic oscillator is an essential tool, widely used in all branches of Physics in order to understand more realistic systems, from classical to quantum and relativistic regimes. 8 Underdamped oscillations are simple harmonic oscillations with an exponentially decaying amplitude.
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