固体介质中细胞自动机有限深势阱的量子力学分析  

The quantum mechanics analysis on the cellular automata finite deep potential trough model in the solid medium

作　　者：赵雪平[1] 杨宝俊[1] 

机构地区：[1]吉林大学,长春130026

出　　处：《地球物理学进展》2006年第1期53-60,共8页Progress in Geophysics

基　　金：国家自然科学基金项目(40374045)资助

摘　　要：在细胞自动机有限深势阱模型的基础上,利用Lennard-Jones(12-6)势能,通过量子力学推导和分析,对模型中的势能和分子组能量的形式和分布进行了探讨.得到了分子组具有微观和宏观的性质的进一步说明(具有微观尺度特性的截断半径系数μ和具有宏观尺度特性的平衡半径系数τ),并讨论了μ和τ的变化对模型势能和能量的影响;得到了模型的Lennard-Jones(10-6)势能函数,并且势能是周期性分布的,在单个势阱中呈“桶”状;推出了分子组能量满足的关系式,并通过分析势能的变化,得到了模型中分子组能量的可能分布和一些规律,分子组的能量具有连续能带(势能为0)和不连续能带(势能不为0)结构;整体上单个势阱中相邻能量的间隔是逐渐增大的.Based on the cellular automata finite deep potential trough model and the Lennard-Jones （12-6） potential, the paper analyses the form and distribution of the potential energy and energy of the molecule group in the model in terms of the deduce of the quantum mechanics. Simultaneously, the paper further illustrates the microscopic and macroscopic characteristics of the molecule group, namely, the cut off radius coefficient μ which has the microscopic quality and the equilibrium radius coefficient τ which has the macroscopic quality, and discusses the influences of the changes of μ and ton the potential energy and energy of the model. Furthermore the paper presents the Lennard-Jones （ 10- 6） potential function, which is periodic distribution and exhibits a ＂bucket＂ in a single potential trough. What＇s more, the paper deduces the formula related to the energy of the molecule group and obtains the possible distribution and some rules of the energy via analyzing the changes of the potential energy, that is, the energy of the molecule group exhibits the structure of the continuous （when the potential energy equals to zero） and discontinuous （when the potential energy equals to nonzero） energy belt and the interval of the neighboring energy is gradually enlarged in a single potential trough on the whole,

关 键 词：细胞自动机 有限深势阱 分子组 量子力学 Lennard—Jones势能 能带结构 

分 类 号：P631[天文地球—地质矿产勘探]