The Supersymmetry And Eigen Energy Spectrum Of A Charged Dirac Particle In A Uniform Constant Magnetic Field And Supersymmetic Quantum Mechanics

The study of the symmetry and eigen energy spectrum of a charged Dirac particle moving in a uniform constant magnetic field is an important task in many fields of physics, such as the observable effects of the neutron star with strong magnetic field, the spin effect and relativistic effect in quantum Hall effect , supersymmetric quantum mechanics and so on.In this paper, based on the opinion that the γ-matrices in Dirac equation have structure and are decomposable, we decompose the γ-matrices into the direct product of the operators in the spin space and the particle-antiparticle space. By using this method, we attain a complete set of commutative operators, a set of quantum numbers and the correspondingly eigen solutions of the Hamiltonian for a charged Dirac particle moving in a uniform constant magnetic field. In addition, the dynamic supersymmetry of the Hamiltonian is unveiled. Spin symmetry breaking and particle-antiparticle symmetry breaking are discussed. and the supersymmetric group operator of the degenerate spin subspace resulting from the spin residual supersymmetry is found.we find that a supersymmetric quantum mechanics system can always associated...