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 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.

THREE-DIMENSIONAL ISOTROPIC PSEUDO-GAUSSIAN OSCILLATORS

2009 ◽  
Vol 20 (07) ◽  
pp. 1103-1111 ◽  
Author(s):  
ION I. COTĂESCU ◽  
PAUL GRĂVILĂ ◽  
MARIUS PAULESCU
Keyword(s):  
Asymptotic Behavior ◽  
Numerical Methods ◽  
Harmonic Oscillator ◽  
Energy Levels ◽  
Three Dimensional ◽  
Finite Energy ◽  
Energy Spectra ◽  
Isotropic Harmonic Oscillator ◽  
Quantum Models

A family of isotropic three-dimensional quantum models governed by isotropic pseudo-Gaussian potentials is proposed. These potentials are defined to have a Gaussian asymptotic behavior but approaching to the potential of the isotropic harmonic oscillator when x → 0. These models may have finite energy spectra with approximately equidistant energy levels that can be calculated using efficient numerical methods based on generating functionals.

PSEUDO-GAUSSIAN OSCILLATORS

2008 ◽  
Vol 19 (10) ◽  
pp. 1607-1615 ◽  
Author(s):  
ION I. COTĂESCU ◽  
PAUL GRĂVILĂ ◽  
MARIUS PAULESCU
Keyword(s):  
Asymptotic Behavior ◽  
Harmonic Oscillator ◽  
Efficient Method ◽  
Bound States ◽  
Energy Levels ◽  
Numerical Calculations ◽  
One Dimensional ◽  
New Family ◽  
Quantum Models

A new family of one-dimensional quantum models is proposed in terms of new potentials with a Gaussian asymptotic behavior but approaching to the potential of the harmonic oscillator when x → 0. These models give rise to approximative equidistant energy levels of bound states and resonances as it is shown using numerical calculations based on an efficient method of generating functionals.

scholarly journals Spectral Concentration for Perturbed Equations of Harmonic Oscillator Type

2000 ◽  
Vol 3 ◽  
pp. 76-85
Author(s):  
B. M. Brown ◽  
M. S. P. Eastham
Keyword(s):  
Harmonic Oscillator ◽  
Finite Number ◽  
Positive Parameter ◽  
Oscillator Type ◽  
Small Positive Parameter ◽  
Sturm Liouville ◽  
Spectral Concentration

AbstractSturm–Liouville potentials of the form xa ƒ(∈x) are considered, where a > 0, ƒ decays sufficiently rapidly at infinity, and ∈ is a small positive parameter. It is shown that there are a finite number N(∈) of spectral concentration points, and computational evidence is given to support the conjecture that N(∈) increases to infinity as ∈ decreases to zero.

scholarly journals Влияние деформации на энергетический спектр и спектр оптического поглощения фуллерена C-=SUB=-20-=/SUB=- в модели Хаббарда

2019 ◽  
Vol 61 (2) ◽  
pp. 395
Author(s):  
А.В. Силантьев
Keyword(s):  
Group Theory ◽  
Hubbard Model ◽  
Symmetry Group ◽  
Energy Levels ◽  
Analytical Form ◽  
Symmetry Reduction ◽  
Energy Spectra ◽  
Symmetry Groups ◽  
Static Fluctuation Approximation ◽  
Static Fluctuation

Abstract —Anticommutator Green’s functions and energy spectra of fullerene C_20 with the I _ h , D _5 d , and D _3 d symmetry groups have been obtained in an analytical form within the Hubbard model and static fluctuation approximation. The energy states have been classified using the methods of group theory, and the allowed transitions in the energy spectra of fullerene C_20 with the I _ h , D _5 d , and D _3 d symmetry groups have been determined. It is also shown how the energy levels of fullerene C_20 with the I _ h symmetry group are split with the symmetry reduction.

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