等权波包与一维简谐振子

Equal weight wave packet and one-dimensional simple harmonic oscillator

以第n个定态波函数为中心 ,将其附近的从第 (n -N)个到 (n +N)个共 2N + 1个定态波函数以等权重1 2N + 1 叠加起来 ,就构成了所谓的等权波包 .波包上任一力学量f的平均值 f在经典极限下有严格的经典对应 .这一结果可用来考察以往用波包讨论量子力学经典极限的得失之处 .本文较系统地研究了一维简谐振子体系 ,给出了若干新结果 ,并澄清了现行教科书中若干不甚正确的说法 .

By equal weight wave packet,we mean that there are 2N+1 successive stationary states,centered at the nth and ranged from the (n-N)th to (n+N)th,superimposed into it with equal weight.Recent research shows that the expectation value of a physical quantity in the wave packet in classical limit converges to the classical quantity.Since this wave packet can be treated exactly, we can use it to examine the previous results related to wave packets,such as the form of classical limit of the mean value of a quantity in the wave packet,classical correspondence of uncertainty relation,relation between classical probability density and the quantum mechanical one,etc.This paper studies aone dimensional simple harmonic oscillator,demonstrating the differences of our results from previous one.