| This thesis firstly systemically introduced some nuclear structure models .Then, relativistic mean field theory (RMF) was introduced intensively and its application for globular nuclear was presented. Lastly we researched the characteristics of pseudospin symmetry. It briefly includes several following aspects:Firstly, we introduced some nuclear models such as liquid drop model, fermi gas model, shell model, project shell model and Bohr model.Secondly, RMF theory was intensively introduced. Dirac equation representing nucleus, Klein-Gordon equation representing mesons, electric-magnetic equation representing photons and their representation for the globular equation with the normal RMF lagrangian representing nuclear, meson and photon.Thirdly, based on RMF theory, the origin of pseudospin symmetry was intensively explained and the conditions which can meet the ideal pseudospinsymmetry were presented. The conditions are ∑ = 0 or (d∑)/(dr)= 0 . Under thecondition of exact pseudospin symmetry, we solve the Klein-Gordon equation and Dirac equation of the particles moving in the Morse-type, Tan~2 (πηr) -type andreflectionless-type scalar and vector potentials, and present the corresponding bound state energy spectra and relativistic wave functions. Similarly, a generalized relativistic harmonic oscillator for spin 1/2 particles is studied. The eigenfunctions and eigenenergies are obtained for the ring-shaped non-spherical harmonic oscillator by solving Dirac equation with equal mixture of vector and scalar potentials in opposite signs, for which pseudospin symmetry is exact. Then the implication of the corresponding quantum numbers is explained. Several particular cases such as the ring-shaped harmonic oscillator, non-spherical harmonic oscillator, and spherical harmonic oscillator are also discussed.
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