薛定谔方程解与引力三体问题过渡共振解的关系
Relation Between Solutions of the Schrödinger Equation with Transitioning Resonance Solutions of the Gravitational Three-Body Problem
摘要：
结果表明，在牛顿引力作用下的三体问题中，一类近似共振解等价于修正的薛定谔方程的量子化解，其量子化解在很宽的质量范围内可以在能态之间转换.在宏观尺度下，共振解通过在其中一个物体上的弱俘获从一种共振类型过渡到另一种共振类型，而在薛定谔方程中，人们得到在不同能量之间过渡的量子化波解。共振跃迁动力学提供了粒子在薛定谔方程中不同能态之间运动的经典模型。这种方法提供了天体和量子力学之间的联系。
英文摘要：
It is shown that a class of approximate resonance solutions in the three-body problem under the Newtonian gravitational force are equivalent to quantized solutions of a modified Schrödinger equation for a wide range of masses that transition between energy states. In the macroscopic scale, the resonance solutions are shown to transition from one resonance type to another through weak capture at one of the bodies, while in the Schrödinger equation, one obtains quantized wave solutions transitioning between different energies. The resonance transition dynamics provides a classical model of a particle moving between different energy states in the Schrödinger equation. This methodology provides a connection between celestial and quantum mechanics.
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