标题： 两个非线性振荡器的重要例子 显示英文标题

标题： Two important examples of nonlinear oscillators

摘要： 我们讨论一个经典的非线性振子，它被证明是一个超可积系统，其中有限运动是准周期振动，无限（散射）运动由双曲函数表示。 该振子可以看作是一个与位置相关的质量系统，我们展示了对于$n=1$情况的一种自然量子化方法，该方法具有形状不变性的因子分解，然后找到了能量谱。 还讨论了其他可以视为简谐振子推广并接受非标准拉格朗日描述的等时系统。 显示英文摘要

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 $n=1$ 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.