College Physics ›› 2020, Vol. 39 ›› Issue (9): 6-8.doi: 10.16854 /j.cnki.1000-0712.190536

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

ZHANG Jun,ZHU Zhan-wu,HE Ze-dong   

  1. School of Science,Hubei University of Automotive Technology,Shiyan,Hubei 442002,China
  • Received:2019-11-22 Revised:2020-04-21 Online:2020-09-20 Published:2020-09-24

Abstract: 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.

Key words: Pauli-Fierz Hamiltonian, gauge transformation, photon, coordinate and momentum representation