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In this paper, we study symmetrical properties of two-dimensional(2D) screened Dirac Hydrogen atom and isotropic harmonic oscillator with scalar and vector potentials of equal magnitude(SVPEM). We find that it is possible for both cases to preserve so(3) and su(2) dynamical symmetries provided certain conditions are satisfied. Interestingly,the conditions for preserving these dynamical symmetries are exactly the same as non-relativistic screened Hydrogen atom and screened isotropic oscillator preserving their dynamical symmetries. Some intuitive explanations are proposed.
In this paper, we study symmetrical properties of two-dimensional (2D) screened Dirac Hydrogen atom and isotropic harmonic oscillator with scalar and vector potentials of equal magnitude (SVPEM). We find that it is possible for both cases to preserve so (3) and su (2) dynamical symmetries provided certain conditions are satisfied. the conditions for preserving these dynamical symmetries are exactly the same as non-relativistic screened hydrogen atom and screened isotropic oscillator preserving their dynamical symmetries. Somewhat explanations are proposed.