On the ground state of two-dimensional electron gas in a quantizing magnetic field

It is shown that the Fermi energy of two-dimensional electron gas in a magnetic field is quantized. Approximate formulas are obtained for the electron ground state energy in weak and strong magnetic fields with consideration for the interaction of electrons at zero temperature. It follows from the results obtained that,depending on the relationship between the problem parameters (electron density, magnetic field intensity, and orbital angular momentum of relative motion), there can occur phase transitions in the electron system. A simple formula is derived, which relates the Landau level occupancy in a strong magnetic field to the orbital angular momentum of the electron pair.