Bound-state spectrum of the hydrogen atom in strong magnetic fields

Abstract

Energies of the bound states of the hydrogen atom in a uniform magnetic field are calculated for field strengths greater or equal to ${B}_{0}\ensuremath{\approx}2.35\ifmmode\times\else\texttimes\fi{}{10}^{9}$ G. The convergent behavior of the quantum excesses (negative quantum defects) makes it possible to determine completely the bound-state spectrum for given values of the field strength $B$ and the azimuthal quantum number $m$. For $|m|=0,1, \mathrm{and} 2$ results are presented which determine to a uniform relative accuracy of at least 0.1% the energies of all bound states for arbitrary field strengths from $\frac{B}{{B}_{0}}=1$ to $\frac{B}{{B}_{0}}=500$ or higher, beyond which the adiabatic approximation is of comparable accuracy.