Hydrogen atom in a high magnetic field

The low-lying energy levels of a hydrogen atom in a uniformly strong magnetic field B (B<1010 G) are calculated in a simple perturbative variational approach which combines the spirit of the variational principle and the conventional perturbation method. The total Hamiltonian is separated into four parts: a one-dimensional hydrogen-atom system; a two-dimensional harmonic-oscillator system; a z-component angular-momentum operator; and a perturbation part which contains an undetermined variable parameter but is independent of B. The first three parts can be solved exactly. The variational parameter introduced in the Hamiltonian can be determined by requiring the energy-correction expansion to converge as fast as possible. It is found that our calculated ground-state energy is in good agreement with those obtained by the previous works that used the wave-function-expansion approach for high magnetic fields up to γ=7 (i.e., 1010 G for atoms)