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

TL;DR

This paper presents an exact algebraic solution for the two-dimensional screened donor states in a magnetic field, using Levi-Civita transformation and operator methods, relevant for 2D electron gases in quantum well structures.

Contribution

It introduces an exact solution approach for 2D screened donor states in magnetic fields using Levi-Civita transformation and algebraic operator methods.

Findings

Exact solutions of Schrödinger equation obtained

Wave-functions constructed via annihilation and creation operators

Applicable to 2D electron gas in quantum well structures

Abstract

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.