Electron states in a two-dimensional ring - an exactly soluble model

An exactly soluble model for a two-dimensional ring is proposed. Using this model, we have obtained analytically the energy spectrum and wavefunctions for a ring in the presence of a uniform magnetic field and a thin magnetic flux. The model can also describe quantum dots, anti-dots, one-dimensional rings and straight two-dimensional wires, which provides an integrated picture for the electron states and their magnetic field response in these geometries. The simplicity and the flexibility of the model make it an ideal tool for the modelling of the Aharonov - Bohm effects and the persistent currents in quantum rings.