非相对论极限下Pauli-Fierz哈密顿量形式浅析

A brief analysis of different form of Pauli-Fierz Hamiltonian in non-relativistic limit

长度规范下的哈密顿量在讨论量子化电磁场(光子)与原子(或分子)相互作用时有着明显优势,即没有物理上不可观测量矢势A,而是电场与偶极矩的乘积.但是不同的文章中出现的长度规范哈密顿量似乎不一样.在本文中,我们从速度规范下的Pauli-Fierz哈密顿量出发,分别得到坐标和动量表象下的长度规范哈密顿量,从而证明它们的等价性.澄清学生在初次学习时的疑惑.

When we discuss the interaction of atoms or molecules with quantized electromagnetic waves(photons),the Hamiltonian in length gauge takes the advantage by replacing the vector potential A by electric filed multiplying the dipole.However,formulas in different papers seem to have different forms.In this paper,we start from Pauli-Fierz Hamiltonian in velocity gauge and obtain the length gauge Hamiltonian in coordinate and momentum representation,respectively,which proves the equivalence between different forms.We hope this could help students to understand the Hamiltonian in different forms.