Two charges on plane in a magnetic field I. “Quasi-equal” charges and neutral quantum system at rest cases

Low-lying bound states for the problem of two Coulomb charges of finite masses on a plane subject to a constant magnetic field B$B$ perpendicular to the plane are considered. Major emphasis is given to two systems: two charges with the equal charge-to-mass ratio (quasi-equal charges) and neutral systems with concrete results for the hydrogen atom and two electrons (quantum dot).