scholarly journals Geometric Models of the Quantum Relativistic Rotating Oscillator

1997 ◽  
Vol 12 (10) ◽  
pp. 685-690 ◽  
Author(s):  
Ion I. Cotăescu
Keyword(s):  
Fine Structure ◽  
Harmonic Oscillator ◽  
Nonrelativistic Limit ◽  
Energy Spectra ◽  
De Sitter ◽  
Continuous Part ◽  
Geometric Models ◽  
Isotropic Harmonic Oscillator ◽  
Sitter Model ◽  
De Sitter Model

A family of geometric models of quantum relativistic rotating oscillator is defined by using a set of one-parameter deformations of the static (3+1) de Sitter or anti-de Sitter metrics. It is shown that all these models lead to the usual isotropic harmonic oscillator in the nonrelativistic limit, even though their relativistic behavior is different. As in the case of the (1+1) models,1 these will have even countable energy spectra or mixed ones, with a finite discrete sequence and a continuous part. In addition, all these spectra, except that of the pure anti-de Sitter model, will have a fine-structure, given by a rotator-like term.

scholarly journals Geometric Models of the Relativistic Harmonic Oscillator

1997 ◽  
Vol 12 (20) ◽  
pp. 3545-3550 ◽  
Author(s):  
Ion I. Cotăescu
Keyword(s):  
Harmonic Oscillator ◽  
Finite Number ◽  
Continuous Spectrum ◽  
Energy Levels ◽  
Nonrelativistic Limit ◽  
Energy Spectra ◽  
De Sitter ◽  
Geometric Models ◽  
Relativistic Harmonic Oscillator ◽  
Quantum Models

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 nonrelativistic limit, even though their relativistic behavior is quite different. Among quantum models we find a set of models with countable energy spectra, and another one having only a finite number of energy levels and in addition a continuous spectrum.

scholarly journals Historical and philosophical reflections on the Einstein-de Sitter model

2021 ◽  
Vol 46 (1) ◽  
Author(s):  
Cormac O’Raifeartaigh ◽  
Michael O’Keeffe ◽  
Simon Mitton
Keyword(s):  
De Sitter ◽  
Sitter Model ◽  
De Sitter Model

scholarly journals 2D relativistic oscillators with a uniform magnetic field in anti-de Sitter space

2021 ◽  
pp. 2150113
Author(s):  
Lakhdar Sek ◽  
Mokhtar Falek ◽  
Mustafa Moumni
Keyword(s):  
Magnetic Field ◽  
Uniform Magnetic Field ◽  
Principal Quantum Number ◽  
Wave Functions ◽  
De Sitter ◽  
Energy Eigenvalues ◽  
Space Deformation ◽  
Klein Gordon ◽  
Sitter Model ◽  
De Sitter Model

We study analytically the two-dimensional deformed bosonic oscillator equation for charged particles (both spin 0 and spin 1 particles) subject to the effect of an uniform magnetic field. We consider the presence of a minimal uncertainty in momentum caused by the anti-de Sitter model and we use the Nikiforov–Uvarov (NU) method to solve the system. The exact energy eigenvalues and the corresponding wave functions are analytically obtained for both Klein–Gordon and scalar Duffin–Kemmer–Petiau (DKP) cases and we find that the deformed spectrum remains discrete even for large values of the principal quantum number. For spin 1 DKP case, we deduce the behavior of the DKP equation and write the nonrelativistic energies and we show that the space deformation adds a new spin-orbit interaction proportional to its parameter. Finally, we study the thermodynamic properties of the system and here we find that the effects of the deformation on the statistical properties are important only in the high-temperature regime.

scholarly journals Note On A Super-Horizon-Scale Inhomogeneous Cosmological Model

1996 ◽  
Vol 173 ◽  
pp. 25-26
Author(s):  
K. Tomita
Keyword(s):  
Large Scale ◽  
Background Radiation ◽  
Theoretical Explanation ◽  
Cosmological Models ◽  
Low Density ◽  
De Sitter ◽  
Number Count ◽  
Microwave Background Radiation ◽  
Sitter Model ◽  
De Sitter Model

Many observations of large-scale and cosmological structures in the universe have been collected, but so far there is no consistent theoretical explanation. In the region within 100 Mpc from us, the observed two-point correlations of galaxies and clusters of galaxies can be described well by low-density homogeneous cosmological models (Bahcall & Cen 1993; Suto 1993). On the other hand, the observed anisotropies of the cosmic microwave background radiation have been explained well by comparatively high-density cosmological models such as the Einstein-de Sitter model (Bunn & Sugiyama 1994). In the intermediate scale, the angular sizes of the cores of quasars have been measured and their redshift dependence has been shown to be more consistent with the Einstein-de Sitter model than with the low-density models (Kellermann 1993). The number count-magnitude relation for remote galaxies supports low-density models with a nonzero cosmological constant (for example, Fukugita et al. 1990), but these models may be inconsistent with the observed distribution of Lyα clouds (Fukugita & Lahav 1991).

scholarly journals Remarks on cosmology

1959 ◽  
Vol 9 ◽  
pp. 533-535
Author(s):  
G. C. Mcvittie
Keyword(s):  
A Priori ◽  
Initial Instant ◽  
De Sitter ◽  
Relativistic Model ◽  
Space Curvature ◽  
Composite Models ◽  
History Of ◽  
Sitter Model ◽  
The Universe ◽  
De Sitter Model

First, I should like to say something about the use of highly specialized models in cosmology. The Einstein—de Sitter model is a relativistic model in which the cosmical constant and the space-curvature constant are both equated to zero. Likewise, the pressure is assumed to be zero throughout the history of the universe, except perhaps at the initial instant. It is well-known that the first two constants can be determined from observation, if not at present, at any rate as the data are refined in the future. Hence, I think it is a weakness to prejudge the issue and assign a priori values. Nor is it self-evident to me that the pressure must always have been zero even if it is zero now. Composite models, with nonzero pressure at first, followed by a zero-pressure condition, need to be examined.

Sign in / Sign up

Export Citation Format

Share Document