Related papers: The relativistic massless harmonic oscillator
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…
We study the generalized harmonic oscillator which has both the position-dependent mass and the potential depending on the form of mass function in a more general framework. The explicit expressions of the eigenvalue and eigenfunction for…
We solve the generalized relativistic harmonic oscillator in 1+1 dimensions in the presence of a minimal length. Using the momentum space representation, we explore all the possible signs of the potentials and discuss their bound-state…
We construct creation and annihilation operators for harmonic oscillators with minimal length uncertainty relations. We discuss a possible generalization to a large class of deformations of cannonical commutation relations. We also discuss…
We introduce a relativistic version of the non-self-adjoint operator obtained by a dilation analytic transformation of the quantum harmonic oscillator. While the spectrum is real and discrete, we show that the eigenfunctions do not form a…
A family of relativistic geometric models is defined as a generalization of the actual anti-de Sitter (1+1) model of the relativistic harmonic oscillator. It is shown that all these models lead to the usual harmonic oscillator in the…
Problems concerning with application of quantum rules on classical phenomena have been widely studied, for which lifted up the idea about quantization and uncertainty principle. Energy quantization on classical example of simple harmonic…
In the paper we investigate the evolution of the relativistic particle (massive and massless) with spin defined by Hamiltonian containing the terms with momentum-spin-orbit coupling. We integrate the corresponding Hamiltonian equations in…
We describe a magnetically driven torsional oscillator that is well suited for teaching the physics of simple harmonic motion using a collection of hands-on, quantitative experiments. The mechanical Q of the system can be tuned using…
Harmonic oscillator, in 2-dimensional noncommutative phase space with non-vanishing momentum-momentum commutators, is studied using an algebraic approach. The corresponding eigenvalue problem is solved and discussed.
The semiclassical treatment of the two-dimensional harmonic oscillator provides an instructive example of the relation between classical motion and the quantum mechanical energy spectrum. We extend previous work on the anisotropic…
A nonrelativistic charged particle moving in an anisotropic harmonic oscillator potential plus a homogeneous static electromagnetic field is studied. Several configurations of the electromagnetic field are considered. The Schr\"odinger…
We provide the classical mechanics of many particles moving in canonically twist-deformed space-time. In particular, we consider two examples of such noncommutative systems - the set of N particles moving in gravitational field as well as…
We examine various generalizations, e.g. exactly solvable, quasi-exactly solvable and non-Hermitian variants, of a quantum nonlinear oscillator. For all these cases, the same mass function has been used and it has also been shown that the…
In this paper, we consider an anharmonic perturbation to the harmonic oscillator in the classical and the quantum regimes. We analyse a relativistic particle subjected to such a potential and then proceed to study a gas of such particles.…
We consider a quantum space with rotationally invariant noncommutative algebra of coordinates and momenta. The algebra contains tensors of noncommutativity constructed involving additional coordinates and momenta. In the rotationally…
A short review of special relativistic dynamics describing a particle acted upon by an arbitrary conservative external force is presented. If the mass of the particle is zero and the force is central then the equations of motion turn out to…
The frequency of a classical periodic system and the energy levels of the corresponding quantum system can both be obtained using action variables. We demonstrate the construction of two forms of the action variable for a one dimensional…
A classical linear oscillator is treated in the small amplitude limit so that it will be approximately relativistic. The oscillator involves a charge particle in a linear potential in classical zero-point radiation. It is found that the…
We reformulate Classical Mechanics as a timeless relativistic theory. Readers are introduced to a new class of reference systems, the binate frames, where physical events are identified with four position-coordinates -- no clocks are used.…