In this work, it is shown that there is an inherent nonlinear evolution in the dynamics of the so-called generalized coherent states. To show this, the immersion of a classical manifold into the Hilbert space of quantum mechanics is employed. Then, one may parameterize the time dependence of the wave function through the variation of parameters in the classical manifold. Therefore, the immersion allows us to consider the so-called principle of analogy, i.e., using the procedures and structures available from the classical setting to employ them in the quantum framework.

中文翻译：

---

量子动力学的非线性描述：广义相干态

这项工作表明，在所谓的广义相干态的动力学中存在固有的非线性演化。为了证明这一点，采用了将经典流形浸入量子力学的希尔伯特空间的方法。然后，可以通过经典流形中参数的变化来参数化波动函数的时间依赖性。因此，沉浸式使我们能够考虑所谓的类比原理，即使用经典环境中可用的过程和结构将其应用于量子框架。