Exact and quasiclassical Green's functions of two-dimensional electron gas with Rashba-Dresselhaus spin-orbit interaction in parallel magnetic field

New exact and asymptotical results for the one particle Green's function of 2D electrons with combined Rashba - Dresselhaus spin - orbit interaction in the presence of in-plane uniform magnetic field are presented. A special case that allows an exact analytical solution is also highlighted. To demonstrate the advantages of our approach we apply the obtained Green's function to calculation of electron density and magnetization