【简答题】![](https://cos-cdn.shuashuati.com/shuashuati-web/2024-0521-0905-00/logo-new-ad743.png)
设有一N个相互作用可以忽略的粒子(可看成质点)组成的系统,在满足经典极限的条件下,巨正则系综的几率分布为
(i) 试证明巨正则系综的总粒子数是N的几率为
其中ZN是总粒子数为N时的正则系综配分函数.
(ii) 证明使P(N)取极大的总粒子数满足下面的关系:
(证明时,直接求lnP(N)的极大更方便.)
(iii) 上式进一步可以化为
N=e-αZ,
其中z为单粒子的配分函数,即
.上述结果说明什么?
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACAAAAAgCAYAAABzenr0AAAA5ElEQVRYR2NkGGDAOMD2M+B0wKpVq9huv/jbxPD/fxwDA4MkhQ59zsDIuEhVgrkuLCzsF7JZOB3QOml5B8P//+UUWoyqnZGxszovsoI4B0xc9gyfzxmZmb2rcsK3IRvWMWm599///7fgcfTz6vwoKWId8B+f75kZGX0q8iK3kugAhur8KJRQxx0FE5fhdQC5UTPqgNEQGA2B0RAYDYHREBgNgaETAuTW96TqG7yt4tbRFhGRIQBqHTP9+8dIoDUMTxqk5AK8zXKYiaDWMYhNpANIaJYPdMdkwLtmpOZnctUPeDkAAP6tmiH1ggTLAAAAAElFTkSuQmCC)
手机使用
![](https://cos-cdn.shuashuati.com/shuashuati-web/2024-0521-0905-00/share-ico-3febd.png)
分享
![](https://cos-cdn.shuashuati.com/shuashuati-web/2024-0521-0905-00/link-f6c98.png)
复制链接
![](https://cos-cdn.shuashuati.com/shuashuati-web/2024-0521-0905-00/weibo-3e538.png)
新浪微博
![](https://cos-cdn.shuashuati.com/shuashuati-web/2024-0521-0905-00/qq-1c308.png)
分享QQ
![](https://cos-cdn.shuashuati.com/shuashuati-web/2024-0521-0905-00/wechat-a78ae.png)
微信扫一扫
微信内点击右上角“…”即可分享
![](https://cos-cdn.shuashuati.com/shuashuati-web/2024-0521-0905-00/report-ico-11843.png)
反馈
![收藏 - 刷刷题](https://cos-cdn.shuashuati.com/shuashuati-web/2024-0521-0905-00/coll-ico-cfcc9.png)
收藏
![](https://cos-cdn.shuashuati.com/shuashuati-web/2024-0521-0905-00/jubao-9c477.png)
举报
参考答案:
![](https://cos-cdn.shuashuati.com/shuashuati-web/2024-0521-0905-00/logo-new-ad743.png)
参考解析:
![](https://cos-cdn.shuashuati.com/shuashuati-web/2024-0521-0905-00/logo-new-ad743.png)