Two important examples of nonlinear oscillators
数学物理
2007-05-23 v1 math.MP
摘要
We discuss a classical nonlinear oscillator, which is proved to be a superintegrable system for which the bounded motions are quasiperiodic oscillations and the unbounded (scattering) motions are represented by hyperbolic functions. This oscillator can be seen as a position-dependent mass system and we show a natural quantization prescription admitting a factorization with shape invariance for the case, and then the energy spectrum is found. Other isochronous systems which can also be considered as a generalization of the harmonic oscillator and admit a nonstandard Lagrangian description are also discussed.
引用
@article{arxiv.math-ph/0505028,
title = {Two important examples of nonlinear oscillators},
author = {José F. Cariñena and Manuel F. Rañada and Mariano Santander},
journal= {arXiv preprint arXiv:math-ph/0505028},
year = {2007}
}