Hamiltonian of an Electron Under an Electromagnetic Field

O. D. Skoromnik, И. Д. Феранчук

The interaction Hamiltonian of an electron and a quasi-monochromatic pulse of a strong quantized electromagnetic field is examined. Canonical transformations of the field variables are found that allow the division of the system's Hamiltonian in two parts. The first one describes the interaction between an electron and a single collective mode of the field. The properties of this mode are defined by the superposition of the modes corresponding to the pulse wave packet. The second part describes the field fluctuations relatively to the collective mode. The field intensity is estimated for which a single-mode approximation can be used for the system's description.

Chun-Fang Li, Qi Wang

Wang Rong

By following approach of Haken who quantizes the light field and making use of the quantisation of the electromagnetic field,this paper quantizes the electron wave field and derives the Hamilonian of interation between the radiation field and the electron wave field.

Earle H. Kennard

Jochen Autschbach

Abstract The interaction between atoms or molecules and electromagnetic (EM) fields underlies all spectroscopic techniques and a great variety of desirable molecular properties. EM fields and EM waves are introduced via the famous Maxwell equations. The scalar and vector potential are defined, and the gauge freedom is outlined. The Coulomb gauge is adopted. The classical Hamiltonian for a charged particle in an EM field is derived, and from this the ‘minimal substitution’ rules for incorporating the fields in the quantum Hamiltonian are obtained. The operators describing the interaction of an electron with static electric and magnetic fields, including the magnetic fields from nuclear spins, are derived, followed by the derivation of the interaction between an electron and an EM wave.

Earle H. Kennard