摘要
Based on the concept of the energy level repulsion, a potential function followed by the energy level particles is suggested. By regarding the energy level fluctuation spectrum as a dynamic system which consists of the pairs of energy level particles behaving as the generalized harmonic oscillator, a generalized Schrdinger equation valid for the nearest neighbor space (NNS) distribution of the levels is established. It turns out that the different kinds of NNS distributions found so far are the solutions of this equation: Both the Poisson type and Wigner type are its eigen solutions whereas the Gaussian unitary ensemble (GUE) type and the Brody type of NNS distribution are its composite solutions. Furthermore, the influences of the small perturbation on the NNS distribution are analyzed.
Based on the concept of the energy level repulsion, a potential function followed by the energy level particles is suggested. By regarding the energy level fluctuation spectrum as a dynamic system which consists of the pairs of energy level particles behaving as the generalized harmonic oscillator, a generalized Schrdinger equation valid for the nearest neighbor space (NNS) distribution of the levels is established. It turns out that the different kinds of NNS distributions found so far are the solutions of this equation: Both the Poisson type and Wigner type are its eigen solutions whereas the Gaussian unitary ensemble (GUE) type and the Brody type of NNS distribution are its composite solutions. Furthermore, the influences of the small perturbation on the NNS distribution are analyzed.
基金
ProjectsupportedbytheNationalNaturalScienceFoundationofChina (GrantNo .2 96 730 2 8)
