二次量子化中单体和两体算符的一种启发式推导  

An intuitive derivation of one-and two-body operators in the second-quantization formalism

作　　者：吴宁 WU Ning(Center for Quantum Technology Research,School of Physics,Beijing Institute of Technology,Beijing 100081,China)

机构地区：[1]北京理工大学物理学院量子技术研究中心,北京100081

出　　处：《大学物理》2022年第2期18-21,37,共5页College Physics

基　　金：国家自然科学基金(11705007)资助。

摘　　要：二次量子化是研究生和高年级本科生量子力学课程中的重要内容.如何从一次量子化中的多粒子哈密顿量及波函数出发,自然地导出二次量子化中由产生和湮没算符表示的单体和两体算符,是一个既关键且又使初学者较难理解的步骤.以全同费米子系统为例,本文给出该步骤的一种自然且具有启发性的推导方法.该方法仅依赖于:多粒子波函数的对称性假设,Fock空间中“真空填充”的概念,以及全反对称多粒子波函数与Fock态的等价性.Second quantization is an important topic in postgraduate and senior undergraduate level Quantum Mechanics course.A key step in the development of the second-quantization formalism is the derivation of one-and two-body operators from the many-particle Hamiltonian and wave functions in the first-quantization language,which is usually difficult to understand for beginners.Taking the case of an assembly of identical fermions as an example,this paper provides a less ad hoc and intuitive derivation based only on the symmetrization postulate,the concept of“filling the vacuum”in the Fock space,and equivalence between the antisymmetrized many-particle wave function and the Fock state.

关 键 词：二次量子化 单体和两体算符 全反对称态 FOCK态 

分 类 号：O413[理学—理论物理]