Variational Approach to Hydrogen Atom in Uniform Magnetic Field of   Arbitrary Strength
  Extending the Feynman-Kleinert variational approach, we calculate the temperature-dependent effective classical potential governing the quantum statistics of a hydrogen atom in a uniform magnetic at all temperatures. The zero-temperature limit yields the binding energy of the electron which is quite accurate for all magnetic field strengths and exhibits, in particular, the correct logarithmic growth at large fields. 
M. Bachmann, H. Kleinert, and A. Pelster