球坐标中三维各向同性谐振子的类经典态  

Near classical states of three-dimensional isotropic harmonic oscillator in spherical coordinate system

作　　者：李兴华[1] 杨亚天[1] 

机构地区：[1]福建师范大学物理与能源学院,福州350007

出　　处：《物理学报》2015年第8期32-38,共7页Acta Physica Sinica

基　　金：国家重点基础研究发展计划(批准号:2011CBA00203);国家自然科学基金(批准号:61275215)资助的课题~~

摘　　要：把坐标平均值随时间的变化和在宏观条件下与经典解相同的量子态定义为类经典态(NCS),并求解球坐标中三维各向同性谐振子的NCS问题,有助于从波动力学角度理解量子到经典过渡的问题.选与经典态相应的大量子数附近的矩形波包作为NCS,得到与经典解一致的结果,但NCS不是惟一的.一个经典态可以有很多NCS与之对应,就像一个热力学态可以有无数力学态与之对应一样,从量子到经典的描述是一个粗粒化和信息丢失的过程.One can easily understand the transition from special relativity to Newton mechanics under the condition of v/c 〈〈 1. But it is not so easy to understand the transition from quantum representation to classical representation from the point of view of wave mechanics. We define such a quantum state as near classical state （NCS）, in which the mean value of coordinates equals the classical solution on a macroscopic scale. We take the NCS for three-dimensional isotropic harmonic oscillator in a spherical coordinate system for example. We take│ NCS） =N＋△N∑n=N-△t=tM-△tM cnt│nll〉=∑nrl cnrl│2nr＋l,l,l〉,and choose cnl=1/2△N＋1 1/2△lM＋1The mean values of coordinates are r^2=Ec1/μωcl[1＋√1-ω^2L^2c1/Ecl^2 cos （2ωt）]tgφEc1/ωlc1[1-√（ωLc1/Ec1）^2]tg（ωt）in this NCS, which are in agreement with the classical solution on a macroscopic scale, where △N/N〈〈1,△lM/lM〈〈1N and IM are determined by the macroscopic state. N =[Ec1/hω],Ec1=1/2μω^2（a^2＋b^2）1M ： [Ld/h], and L^l = μwab.Here #, Eel and Lcl respectively denote the mass, the energy and the angular momentum of harmonic oscillator. And the bracket [c] means taking the integer part of the number c, for example [2.78] = 2. It is also emphasized that for a definite macro state, there are many NCS corresponding to a macro state; just like the case in statistical physics, many micro dynamical states correspond to a macro thermodynamic state. Thus the transition from quantum representation to classical representation is a coarse-graining process and also an information losing process.

关 键 词：量子经典对应 类经典态 三维谐振子 

分 类 号：O413.1[理学—理论物理]