Quantum Mechanics Analysis Of Ring-shaped Atomic Core Polarization Potential

The atomic core of both hydrogen-like ion and alkali metal is a spherically symmetric structure. When valence electron moves near atomic core, atomic core is polarized in the valence electron field, producing dipole and attracting electron. So the action potential of atomic core on valence electron isConsidering that part of Coulomb potential will be shielded, here0 <η≤1.But practical problems tend to deviate from atomic core polarization models, and it is worth studying some atomic core polarization models which can be strictly solved. Ring-shaped atomic core polarization potential is that atomic core polarization potential pluses ring-shaped inverse squares potential. This model was proposed on the basis of the structure similar to benzene molecule. Recently many physics workers at home and abroad have discussed the problems of ring-shaped oscillator quantum mechanics from all aspects.Based on the above, the thesis proposes a kind of ring-shaped atomic core polarization potential:In this thesis, firstly "N-U method" which is widely applied in solving wave function and energy levels of complex atomic-molecule system at home and abroad in recent years is briefly introduced. Next Schr?dinger equation of ring-shaped atomic core polarization potential is separated in the spherical coordinates. Then on the basis of Second-Order Linear Ordinary Differential Equation, angular wave function equation and axial equation of Schr?dinger equation are solved; angular wave function expressed in terms of ultra-spherical Polynomials and axial wave function expressed in terms of confluent hyper-geometric function and the exact energy levels equation are obtained as well under the application of special function and"N-U method".Under the condition of equal scalar and vector potentials, angular wave function and axial wave function and the exact energy levels equation for the above ring-shaped atomic core polarization potential are obtained by solving Dirac equation. And the result for solutions of Schr?dinger equation and Dirac equation is briefly discussed in this thesis.Actually, from the mathematical point of view, stationary state Schr?dinger equation and Dirac equation for the above ring-shaped atomic core polarization potential are relatively strictly solved in this thesis by applying N-U method.