Wavefunctions for a hydrogen atom in a magnetic field based on some local properties

Abstract

We have analysed some local properties of the energy eigenfunctions of a hydrogen atom in a magnetic field, in the domains where the electron is close to, or far away from, the nucleus. Based on these local properties, we have developed simple, model energy eigenfunctions for the ground state, for the lowest energy m = 0 odd z-parity state, and for the lowest energy m = -1 state. These parameter-free wavefunctions predict fairly accurate values for the energies over the entire range of the magnetic field, and provide a clear insight into the physical structure of the wavefunctions.