相关论文: Harmonic Oscillators as Bridges between Theories: …

This paper is based on MacColl's [1] solution of the equation of motion for a linear (harmonic) oscillator subject to the laws of special relativity in the rest frame of the center of attraction. MacColl's result can be extended to the…

The system of two-dimensional damped harmonic oscillator is revisited in the extended phase space. It is an old problem already addressed by many authors that we present here in some fresh points of view and carry on smoothly a whole…

Lorentz-covariant harmonic oscillator wave functions are constructed from the Lorentz-invariant oscillator differential equation of Feynman, Kislinger, and Ravndal for a two-body bound state. The wave functions are not invariant but…

We investigate the convergence properties of a perturbation method proposed some time ago and reveal some of it most interesting features. Anharmonic oscillators in the strong--coupling limit prove to be appropriate illustrative examples…

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…

For a harmonic oscillator with time-dependent (positive) mass and frequency, an unitary operator is shown to transform the quantum states of the system to those of a harmonic oscillator system of unit mass and time-dependent frequency, as…

The Courant-Snyder theory for two-dimensional coupled linear optics is presented, based on the systematic use of the real representation of the Dirac matrices. Since any real $4\times 4$-matrix can be expressed as a linear combination of…

We discuss the Dirac oscillator in $(1+1)$ and $(2+1)$ dimensions and generalize it in the spirit of the isotonic oscillator using supersymmetric quantum mechanics. In $(1+1)$ dimensions, the Dirac oscillator returns to the quantum harmonic…

Synchronization is studied in an array of identical oscillators undergoing small vibrations. The overall coupling is described by a pair of matrix-weighted Laplacian matrices; one representing the dissipative, the other the restorative…

The fundamental quantum dynamics of two interacting oscillator systems are studied in two different scenarios. In one case, both oscillators are assumed to be linear, whereas in the second case, one oscillator is linear and the other is a…

The Levi-Civita transformation is applied in the two-dimensional (2D) Dirac and Klein-Gordon (KG) equations with equal external scalar and vector potentials. The Coulomb and harmonic oscillator problems are connected via the Levi-Civita…

The response of a test particle, both for the free case and under the harmonic oscillator potential, to circularly polarized gravitational waves is investigated in a noncommutative quantum mechanical setting. The system is quantized…

Relations between Hamiltonian mechanics and quantum mechanics are studied. It is stressed that classical mechanics possesses all the specific features of quantum theory: operators, complex variables, probabilities (in case of ergodic…

We study the known coherent states of a quantum harmonic oscillator from the standpoint of the original developed noncommutative integration method for linear partial differential equations. The application of the method is based on the…

Two harmonic oscillators interacting through the exchange of a quantum field leads to non-zero entanglement between the two, which is absent for classical interaction. In this work, we determine the entanglement between two such harmonic…

We develop an approach to study the entanglement in two coupled harmonic oscillators. We start by introducing an unitary transformation to end up with the solutions of the energy spectrum. These are used to construct the corresponding…

The standard quantum mechanical harmonic oscillator has an exact, dual relationship with a completely classical system: a classical particle running along a circle. Duality here means that there is a one-to-one relation between all…

The Schr\"odinger equations for the Coulomb and the Harmonic oscillator potentials are solved in the cosmic-string conical space-time. The spherical harmonics with angular deficit are introduced. The algebraic construction of the harmonic…

The subject of this work is to apply the modified Feynman disentangling approach to a problem of transitions in a non-quadratic quantum-mechanical system: a singular oscillator with a time-dependent frequency.

When Einstein formulated his special relativity, he developed his dynamics for point particles. Of course, many valiant efforts have been made to extend his relativity to rigid bodies, but this subject is forgotten in history. This is…