Effect of a crossed uniform electromagnetic field on loosely localized electron states

An approximate analytic solution for the ground electron state is found to the Schrodinger equation for a combination of a uniform magnetic field and a single attractive -lambda delta(r) potential. The effect of the magnetic field on this loosely localized electron state is studied. We show that this effect leads to the appearance of the probability current density in some region centered at the point r = 0 as well as changing the localization region of electron in the plane perpendicular to the magnetic field. The effect of a constant crossed uniform electromagnetic field on the loosely localized electron state is also discussed.