Relativistic harmonic oscillator, the associated equations of motion, and algebraic integration methods

2013 ◽  
Vol 87 (3) ◽  
Author(s):  
D. Babusci ◽  
G. Dattoli ◽  
M. Quattromini ◽  
E. Sabia
Keyword(s):  
Harmonic Oscillator ◽  
Equations Of Motion ◽  
Integration Methods ◽  
Relativistic Harmonic Oscillator

On the constant of motion of dissipative systems

2002 ◽  
Vol 80 (1) ◽  
pp. 1-5 ◽  
Author(s):  
A Patiño ◽  
H Rago
Keyword(s):  
Harmonic Oscillator ◽  
Equations Of Motion ◽  
Viscous Medium ◽  
Dissipative Systems ◽  
Damped Harmonic Oscillator ◽  
Constant Of Motion

We apply results on symmetries of equations of motion and equivalent Lagrangians to obtain a constant of motion for a particle travelling through a viscous medium and for the damped harmonic oscillator. PACS No.: 45.20Jj

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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