Localized impurity embedded in a two-dimensional electron gas

The problem of a localized impurity embedded in a free-electron gas is examined in the case when the gas forms a two-dimensional circular disc instead of filling a three-dimensional sphere. The phase shifts obtained in the disc provide us with a different behavior of the displaced electron charge, residual resistance, electronic specific heat, spin paramagnetism, and electric thermopower than observed in the case of a three-dimensional electron gas perturbed by a localized impurity having the same potential strength. A difference in the dependence of the Knight shift on the distance from the impurity position is also examined. If the spin polarization of the electron gas by an impurity is admitted, this polarization is found to be easier in a three-dimensional than in a two-dimensional electron gas.