, or, what is the same thing, we must haveZürich
11 June 1926
My dear Professor,
Please do not be annoyed with me because I am just today answering your extremely kind letter of the 4th of June. I have written to Mr. Grüneisen in the meantime that I now finally accept for July 16th, and in fact it also suits me excellently because then I need to conclude my lectures a few days earlier, and besides, these last lectures are no longer worth much, since the men already have their heads full of the vacation. I am very sorry, however, not to be able to see or to become acquainted with Mr. Grüneisen himself, but unfortunately that can’t be helped.
Now first and foremost my very hearty thanks for your kind invitation to stay with you which I of course accept with the utmost pleasure. The words with which you offer me your house as a “place of refuge from Berlin” express a boundless, thoughtful, concerned kindness that has truly touched me. You are quite correct that one is most often in want of just this possibility of being alone for a few hours in situations where everyone around is striving to be nice to one. I hope, however, that I will not need to make much use of this possibility in the present situation, despite my end-of-semester fatigue. Not only would I really like to give as much as I possibly can, both in and outside the “official” hours, to the gentlemen in Berlin who are so friendly as to be interested in my work; but also from a purely selfish standpoint I should like to make full and intensive use of the opportunity to discuss the things that have held me completely captured for months, with a number of the most distinguished scientists with the widest variety of research interests. If one still gets a little tired after a few days—the pleasure of the interesting dialogues would be sufficient compensation, to say nothing of the stimulation and the positive challenge.
I will hold to your advice for which I am very grateful, concerning the general lecture, and will naturally be very happy if anyone still has the desire to listen to me on the following day in the more restricted group.
By the way, during the last few days another heavy stone has been rolled away from my heart: I have the interaction of the atom with an incident light wave, thus the theory of dispersion. I had considerable anxiety over it because it was to be feared that the eigenfrequencies themselves would appear as the locations of the resonances in the case of a forced oscillation, and furthermore, that the forced vibrations would not depend on the existing nearby proper oscillations, i.e. not on the state in which the atom happens to be. And that would be nonsense. But it all resolved itself with unheard of simplicity and unheard of beauty; it all came out exactly as one would have it, quite straightforwardly, quite by itself and without forcing. This is the way: what I called the “wave equation” up to now is really not the wave equation but rather the equation for the amplitude. It no longer contains the time at all, but instead of it, it already has an integration constant E, (see Eq. [18″] of my second paper.) The time dependence must be given by , or, what is the same thing, we must have
One can eliminate E from this equation and equation (18″) and one thus obtains the true wave equation which is of fourth order in the coordinates, perhaps of the type of the vibrating plate.
The main point is now this: one may now in a free and easy way also let the potential energy be an explicit function of the time in this true wave equation. The interaction energy with the incident wave can be added on as a perturbing term, and perturbation theory straightforwardly applied, which is quite simple. The result is essentially the so-called Kramers dispersion formula, with completely exact assertions about the phase and polarization of the secondary radiation, naturally assuming that the eigenfunctions and eigenvalues of the unperturbed atom are known.
What is still missing from the whole picture is only the interaction with its own wave, i.e. what corresponds to radiation damping. I believe that can no longer be very hard.
Naturally, perturbation theory can still be applied to many other questions too, e.g. the perturbation due to an α-particle or an electron flying past. I believe that it is a rather considerable step forward because the whole course of an event in time can now be exactly followed—at least in principle.
I should like to arrive in Berlin on the evening of July 15th, if that is agreeable to you; i.e. if it can be so arranged that the train does not arrive much too late. I will have to study the very many different possibilities first, and then I will let you know definitely. In the meantime, my warmest thanks once again to you and your wife for your great kindness. Please do not put yourself out at all; the less trouble I give you the happier I will be!
With sincere respect, I am always
Yours,
E. Schrödinger