Highly Accurate Solution for a Hydrogen Atom in a Uniform Magnetic Field

Abstract

The highly accurate series solution for a hydrogen atom in a uniform magnetic field of arbitrary strength is obtained. It is derived in the form of a power series in two variables, the radius and the sine of the cone angle, with explicit recurrent relations for the coefficients of the power series. As an illustration, a brief list of energy values with accuracy ${10}^{\ensuremath{-}12}$ hartree for the magnetic field $0<B/({m}_{e}^{2}{e}^{3}c/{\ensuremath{\Elzxh}}^{3})\ensuremath{\le}4000$ and pictures of selected anticrossings in the chaotic region of the spectrum are presented.