Papers
Release Time: 2025-04-30Hits:
- Date:2025-04-30
- Title of Paper:A novel kind of equations linking the quantum dynamics and the classical wave motions based on the catastrophe theory
- Journal:Europhysics Letters
- Summary: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.
- Co-author:Jiu Hui Wu, Lin Zhang, and Kejiang Zhou
- Volume:Vol.136, No.4, 2021
- Page Number:40004 (4 Pages)
- Translation or Not:No
- Date of Publication:2021-08-06
