含时薛定谔-牛顿方程的变分方法
Variational approach to the time-dependent Schrödinger-Newton equations
摘要：
使用基于拉格朗日公式和高斯试验函数的变分方法，我们推导出一个简单的动力系统，该系统捕获了依赖于时间的薛定谔-牛顿方程的主要特征。该模型只需要很少的分析或数值计算工作，就可以得到关于基态密度和能量本征值、线性频率以及非线性长时间行为的信息。我们的结果是在良好的协议，通过分析估计或数值模拟的完整的薛定谔-牛顿方程。
英文摘要：
Using a variational approach based on a Lagrangian formulation and Gaussian trial functions, we derive a simple dynamical system that captures the main features of the time-dependent Schrödinger-Newton equations. With little analytical or numerical effort, the model furnishes information on the ground state density and energy eigenvalue, the linear frequencies, as well as the nonlinear long-time behaviour. Our results are in good agreement with those obtained through analytical estimates or numerical simulations of the full Schrödinger-Newton equations.
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