單電子粒子之迪拉克方程式經佛迪-吾速森轉換的漢米爾敦量與托馬仕-班傑明-麥克-特勒第方程式的關係

Abstract

The classical Hamiltonian of a point charged particle with intrinsic spin, which is composed of the relativistic orbit Hamiltonian and the spin Hamiltonian. This spin Hamiltonian can be derived from the Thomas-Bargmann-Michel-Telegdi equation. In our thesis, we will prove that the classical Hamiltonian in which the gyromagnetic ratio equals 2 is in agreement with the low-energy limit of the Dirac equation, the relativistic quantum theory for a spin-1/2 charged particle. For this purpose, we apply the Foldy-Wouthuysen transformation to the Dirac Hamiltonian under the assumptions of the static and homogeneous electromagnetic fields. Furthermore, in order to maintain such a correspondence in arbitrary gyromagnetic ratio cases, we perform the F-W transformation to the Dirac-Pauli Hamiltonian, which is the Dirac Hamiltonian plus the anomalous magnetic dipole moment Hamiltonian. Up to the twelfth-order of F-W transformed Dirac and Dirac-Pauli Hamiltonian, the calculation results are in accord with the corresponding classical Hamiltonians.