A novel kind of equations linking the quantum dynamics and the classical wave motions based on the catastrophe theory
发布时间：2025-04-30
点击次数：
- 发布时间：
- 2025-04-30
- 论文名称：
- A novel kind of equations linking the quantum dynamics and the classical wave motions based on the catastrophe theory
- 发表刊物：
- Europhysics Letters
- 摘要：
- Considering that the catastrophe theory could describe quantitatively any phase transition process, we adopt the folding and cusp catastrophe types as the potential function in the Schrödinger equation to attempt to link the quantum dynamics and the classical wave motions, respectively. Thus through the dimensionless analysis a novel kind of partial differential equations is derived out. When the scaling parameter of the novel equation is equal to the Plank’s constant, this equation becomes a detailed time-independent Schrödinger equation, from which Bohr correspondence principle can be found. On the other hand, when the scaling parameter tends to zero, this equation could degenerate to the classical Helmholtz equation. Therefore this novel kind of equations could describe quantitatively the variation process of the wave functions from the macroscopic level to the quantum size.
- 合写作者：
- Jiu Hui Wu, Lin Zhang, and Kejiang Zhou
- 卷号：
- Vol.136, No.4, 2021
- 页面范围：
- 40004 (4 Pages)
- 是否译文：
- 否
- 发表时间：
- 2021-08-06