scholarly journals Pseudospin symmetry and the relativistic harmonic oscillator

2004 ◽  
Vol 69 (2) ◽  
Author(s):  
R. Lisboa ◽  
M. Malheiro ◽  
A. S. de Castro ◽  
P. Alberto ◽  
M. Fiolhais
Keyword(s):  
Harmonic Oscillator ◽  
Pseudospin Symmetry ◽  
Relativistic Harmonic Oscillator

scholarly journals PERTURBATIVE BREAKING OF THE PSEUDOSPIN SYMMETRY IN THE RELATIVISTIC HARMONIC OSCILLATOR

2004 ◽  
Vol 13 (07) ◽  
pp. 1447-1451 ◽  
Author(s):  
RONAI LISBOA ◽  
MANOEL MALHEIRO ◽  
A. S. de CASTRO ◽  
P. ALBERTO ◽  
MANOEL FIOLHAIS
Keyword(s):  
Harmonic Oscillator ◽  
Neutron Stars ◽  
Bound States ◽  
Pseudospin Symmetry ◽  
Positive Energy ◽  
Relativistic Harmonic Oscillator ◽  
Tensor Potential ◽  
Mean Fields ◽  
Energy Bound ◽  
Shed Light

We show that relativistic mean fields theories with scalar S, and vector V, quadratic radial potentials can generate a harmonic oscillator with exact pseudospin symmetry and positive energy bound states when S=-V. The eigenenergies are quite different from those of the non-relativistic harmonic oscillator. We also discuss a mechanism for perturbatively breaking this symmetry by introducing a tensor potential. Our results shed light into the intrinsic relativistic nature of the pseudospin symmetry, which might be important in high density systems such as neutron stars.

Pseudospin symmetry in the relativistic harmonic oscillator

2005 ◽  
Vol 757 (3-4) ◽  
pp. 411-421 ◽  
Author(s):  
Jian-You Guo ◽  
Xiang-Zheng Fang ◽  
Fu-Xin Xu
Keyword(s):  
Harmonic Oscillator ◽  
Pseudospin Symmetry ◽  
Relativistic Harmonic Oscillator

The quantum relativistic harmonic oscillator: generalized Hermite polynomials

1991 ◽  
Vol 156 (7-8) ◽  
pp. 381-385 ◽  
Author(s):  
V. Aldaya ◽  
J. Bisquert ◽  
J. Navarro-Salas
Keyword(s):  
Harmonic Oscillator ◽  
Hermite Polynomials ◽  
Relativistic Harmonic Oscillator

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.

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