CAJ | 학술논문

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。
파좌표평균치수시간적변화화재굉관조건하여경전해상동적양자태정의위류경전태(NCS),병구해구좌표중삼유각향동성해진자적NCS문제,유조우종파동역학각도리해양자도경전과도적문제。선여경전태상응적대양자수부근적구형파포작위NCS,득도여경전해일치적결과,단NCS불시유일적。일개경전태가이유흔다NCS여지대응,취상일개열역학태가이유무수역학태여지대응일양,종양자도경전적묘술시일개조립화화신식주실적과정。
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??N lM∑+?lM l=lM??lM cnl|nll?=∑nr l cnr l|2nr+l, l, l?, and choose cnl=1 2?N+1 1 2?lM +1 . The mean values of coordinates are r2= Ecl μω2 ( 1+√1? ω2L2cl E 2cl cos(2ωt) ) and tg?= Eclωlcl [ 1?√1?(ωLcl Ecl )2 ] tg(ωt) in this NCS, which are in agreement with the classical solution on a macroscopic scale, where?N/N ?1,?lM/lM ?1. N and lM are determined by the macroscopic state. N =[ Ecl~ω] , Ecl = 12 μω2(a2+b2), lM =[Lcl/~], and Lcl =μωab. Here μ, Ecl 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.