Some Spin-orbit Coupling Effects On Anisotropic Quantum Dots

In quantum mechanics,there are very few systems whose propagators can be obtained exactly,especially when spin-orbital coupling(SOC)effects are taken into account.In chapter 2 by using the group theoretical method on phase space,we derive analytical expressions for the propagators of anisotropic quantum dots with atomic SOC.In chapter 3we apply the propagator to study the evolution of spin-dependent Gaussian wave packets.It is shown that the cylinder symmetry for the probability densities,electron densities and z component of spin-densities of the Gaussian wave packets in the anisotropic cases are broken and have quite different behaviors from the isotropic cases,while in the latter cases the cylinder symmetries are remained all the times.In order to further see the anisotropic effects,in chapter 4 we investigate the absorption spectra,and anisotropic quantum dot are obviously different from isotropic dot.