The energy structure of free electrons for semiconductor in the field of cylindrical symmetry

Abstract

The energetic structure of semiconductor free electrons in the field of cylindrical symmetry whose radial part is a sum of two components, which depend on radial coordinate according to quadratic and biquadratic laws has been studied. The quantization conditions for energy in this field are found and the importance of both quadratic and biquadratic component quantum state formation is analyzed. It is shown that these states can be described by generalized degenerated hypergeometric functions. It is revealed that presence of the biquadratic component is important for the structure of energy levels.