ON THE BOUND-STATES OF A CHARGED, NONRELATIVISTIC PARTICLE IN THE FIELD OF A STATIONARY MAGNETIC DIPOLE - AN INTRODUCTION

The motion of ions above the earth's atmosphere is introduced by discu ssing the nonrelativistic motion of a charged particle in the field of a stationary magnetic dipole. Unlike the Kepler or Coulomb problem, n o way is known to separate our problem into one-dimensional problems a nd a fortiori an exact analytic solution is not known. However, an eff ective potential can be identified whose study clarifies the qualitati ve and semiquantitative features of the bound states. We ask about the periodicity of bound states, taken for granted by one exposed only to the Kepler or Coulomb problem, and show how consideration of phase sp ace can provide a partial answer, Poincare recurrence. The treatment i s accessible to students who have a first acquaintance with the canoni cal formalism and Liouville's theorem, for example first-year graduate students. (C) 1996 American Association of Physics Teachers.