Expansions of a plane wave in Landau states are derived corresponding to an adiabatic and to a sudden switching on of the magnetic field. Two earlier solutions given by Faisal (1982) and by Ohsaki (1983) are found to be valid alternative expansions in the adiabatic case, which differ only in the choice of normalisations of the basis states used. A result identical to Ohsaki's is reobtained, since the Landau states are confined by conservation of energy to a large but finite area L_xL_y approximately 1/ gamma , perpendicular to the field. This energy conservation requires the corresponding sum over the degenerate Landau states to be restricted within a finite range. The upper and lower limits of this range are derived. The completeness relation of Faisal's expansion shows that it is also effectively and automatically confined to the same range of states. In the limit gamma to 0 both sets of expansion coefficients become identical and the results go over to the desired plane-wave state. In the sudden case, when the field switches instantaneously from zero to a finite value, the expansion no longer consists of Landau states of a fixed energy, and the result is new. The two results correspond to different limiting cases of any experimental situation, and the sudden expansion is shown to be invalid at the highest laboratory field ( approximately 20 kG) in current use. The experimental situations corresponding to the two different expansions are discussed.