已知<img src="https://static.zxtiku.com/wangke/imgs/topic/f50203b5d83db06ba7db38580a319c08.png"/>为谐振子升降算符，<img src="https://static.zxtiku.com/wangke/imgs/topic/db1ef8bba77d16ef0997eb28080d51ea.png"/>为粒子数算符，分别满足<img src="https://static.zxtiku.com/wangke/imgs/topic/3a1b4348697bf0787a1b9b271beecdf6.png"/>，则有<img src="https://static.zxtiku.com/wangke/imgs/topic/b6c4c29f9cd3270590a39c645466e30f.png"/>______________<img src="https://static.zxtiku.com/wangke/imgs/topic/01a3e1935af7b7c53461e73d062d0492.png"/>‎