The energy levels and eigen wave functions of electrons in quantum rings in the magnetic field

Abstract

The solution of the eigenvalue problem for non interacting electrons of the quantum ring in the magnetic field is discussed. The potential shape of the quantum ring permitting analytical solution was proposed. The solution of the appropriate eigenvalue problem was found in the terms of the Heun functions and expression for the energy levels was obtained. It was pointed out that proposed potential might be considered as a single-well or double-well potential of concentric quantum rings.

Keywords

• quantum ring
• magnetic field
• quasi-exactly solvable models of quantum mechanics