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

We have analysed some local properties of the energy eigenfunctions of a hy drogen 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 hav e developed simple, model energy eigenfunctions for the ground state, for t he lowest energy m = 0 odd z-parity state, and for the lowest energy m = -1 state. These parameter-free wavefunctions predict fairly accurate values f or the energies over the entire range of the magnetic field, and provide a clear insight into the physical structure of the wavefunctions.