Exact Treatment of the Ground States of Three Two-Dimensional Contact Interactions in a Uniform Magnetic Field

Abstract

The Green function for an electron confined to a plane in the presence of a uniform perpendicular magnetic field is derived and is decorated by several modified Dirac delta functions (MDF). In each case the ground state energy is examined as a function of the field strength, the spacing and the coupling constant of the MDFs. The results suggest that the magnetic field is ionising and the strength of the MDFs must attain a field-dependent critical value in order that a bound state be formed. This offers a new perspective on the question of whether a static magnetic field can be ionising.