Landau level mixing by full spin-orbit interactions

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We study a two-dimensional electron gas in a perpendicular magnetic field in the presence of both Rashba and Dresselhaus spin-orbit interactions. Using a Bogoliubov transformation we are able to write an approximate formula for the Landau levels, thanks to the simpler form of the resulting Hamiltonian. The exact numerical calculation of the energy levels, is also made simpler by our formulation. The approximate formula and the exact numerical results show excellent agreement for typical semiconductors, especially at high magnetic fields. We also show how effective Zeeman coupling is modified by spin-orbit interactions.