Wave functions of a hydrogen atom are obtained under such an assumption that the hydrogen atom is perturbed successively by moving ions in a plasma. Due to the thermal motion of ions, the perturbation field around the atom is a time-dependent one so that the wave functions of the atom correspond no energy eigenfunction. However, they are expressed by linear combinations of the eigenfunctions of an unperturbed atom; the wave functions throughout the life time of the energy level of the atom are determined so as to satisfy the Schrödinger equation including the perturbation Hamiltonian.
From these wave functions, the profile of the Lymann alpha line emitted from a certain hydrogen atom is calculated.Using the result of this calculation, the line profile observed by experiment is obtained by a statistical treatment where the profile of the line emitted from a certain atom is averaged over all possible velocities of the perturbing ion and its closest distance to the atom. Because no restriction is imposed upon the, range of the temperature and the ion density of the plasma, the obtained result is a most general one.
In the one extreme case where the temperature of the plasma is low and the ion density is high, the present theory gives results coincident with those of the quasi-static theory. In the other extreme case, that is, in the case of the plasma of high temperature and low ion density, the present theory shows that the line profile coincide with a Lorentzian one predicted by the impact theory.
As a result of a detailed discussion concerning to the half-half width of the line in the latter case, it is shown that the width is given by a sum of three components which are related to three types of interaction between the light emitting atom and the perturbing ion; they are called optical collision, intermediate range interaction and long range interaction. Of course, the optical collision means the interaction which produces a large phase change in the wave function of the atom. On the contrary, remaining two types of interaction have such a common character that they cause a small phase change; hence, they are generally callcd weak interaction. They are distinguished with each other by the magnitude of the closest distance between the atom and the ion; when the closest distance is much smaller than the mean distance between ions, the interaction is called intermediate range interaction, on the other hand, when the closest distance is the same order of magnitude as the mean distance, the interaction is called long range one.
When the temperature of the plasma is extremely high and the ion density is extremely low, the effect of the intermediate range interaction predominate so that the half-half width is determined by this effect. This fact means that the classical impact theory is not applicable in this case. Furthermore, this fact gives reasons for the fundamental hypothesis assumed in the advanced impact theory proposed recently by Griem et al.
However, the author does not agree to the method of calculation and the application to the actual problem developed by them.
When the temperature of the plasma is somewhat lower and the ion density is somewhat higher compared with those in the case described above, the three components of the half-half width relating to the three types of interaction are of same order of magnitude. Therefore, the line profile is interpreted semiquantitatively by the classical impact theory in this case. However, it should be noted that this fact never means that only the effect of the optical collision is significant and the effect of the weak interaction is negligible.

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