Exact Solution of Two-Dimensional Screened Donor State in a Magnetic Field

The use of Levi-Civita transformation allows us to formulate the problem of two-dimensional screened donor states in a magnetic field as that of two-dimensional anharmonic oscillator. Therefore, the operator method can be directly used for the first problem and the exact solutions of Schrodinger equation are obtained correspondently. In our approach, wave-functions are constructed in the representation of annihilation and creation operators, which permits one to use purely algebraic method in further calculations of other characteristics. The considered problem is related to the motion of 2D electron gas in GaAs/AlGaAs multiple-quantum well structures with the presence of a magnetic field, which continues to provide new and fascinating phenomena.