量子力学角动量算符的压缩态表象

Squeezed state representation of angular momentum operators in quantum mechanics

我们注意到角动量上升、下降算符在绕第三轴的转动变换下呈现压缩变换的特性,故而对照双模压缩变换的特性寻求角动量算符的新的玻色算符实现.通过建立量子力学两体纠缠态表象后,我们发现了一类新的玻色实现,从而可以用压缩的观点来表述量子转动.我们还研究了在这种表示下角动量上升、下降算符对纠缠态表象作用的结果和应用.这说明在量子力学课堂教育中,引入纠缠态表象是必要的.按照本文的思路,还可以构建多粒子纠缠态表象并发现角动量的多模玻色实现.

We notice that the angular momentum raising and lowering operators exhibit squeezing transformation property under rotating around the third axis,sOwe compare this with two-mode squeezing operator tOfind new Bose realization of angular momentum operators.By observing the quantum mechanical bipartite entangled state representation,we find the new Bose realization of angular momentum operators,which enables us tOview quantum rotation as squeezing.We alsOstudy the new raising and lowering operators’character in the entangled state representation.This shows that the entangled state representation is of necessity tOteaching quantum mechanics.We expect that new multi-partite entangled state representation can be constructed and multi-mode Bose realization of angular momentum operator can be found.