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Supersymmetric Quantum Mechanics in Central Situation Field and Solving of Dirac Equation in Magnetic Field

Author: ZuoXiuMing
Tutor: HuXianQuan
School: Chongqing Normal University
Course: Theoretical Physics
Keywords: Supersymmetric quantum mechanics Superpotential Witten index Supersymmetry breaking Singular superpotential
CLC: O413.1
Type: Master's thesis
Year: 2011
Downloads: 30
Quote: 0
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Abstract


Hydrogen-like ions and alkali metal atom of an element is actually a spherically symmetric structure, and its potential field has a circular symmetry. However, it is atomic valence electrons are polarized field , off-center form dipoles attract electrons, atoms in solid role on the valence electron Coulomb potential part of the shielding effect of the potential can become a fact table , often polarized atoms form a very real model , the study can be solved exactly on the atomic core polarization model has a very important significance. People in order to study the molecular structure of benzene similar model, a real ring atom interaction potential , that is the real role of the original atomic potential plus a ring on the inverse square potential . Such model is called domestic workers in physics research hotspot , and all aspects of the ring oscillator quantum mechanics . This paper consists of three aspects: first , first introduced in recent years at home and abroad have been widely used to solve complex atomic and molecular systems Supersymmetric Quantum Mechanics method ( referred SUSTQM method ) and then study the real polarization potential in the ring atoms under the radial Schr?dinger equation spherical coordinate system for separation of variables , respectively, supersymmetric quantum mechanics method for solving equations radial and angular spectra and wave function equation . Second, supersymmetric quantum mechanics under the uniform magnetic field Dirac equation is solved , the Dirac equation γ? Matrix factorization positive and negative particle spin space and space operators direct product , and seek the Hamiltonian of the Zheng Xie , and discuss Supersymmetry and charged particles intrinsic spectrum . Third, we define an index based on Witten discuss supersymmetry breaking problems and singular potentials under breaking . Finally, we propose outlook .

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CLC: > Mathematical sciences and chemical > Physics > Theoretical Physics > Quantum theory > Quantum mechanics ( wave mechanics,matrix mechanics )
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