8 April 1926
My dear Professor,
I was indescribably delighted by your kind card of April 2nd. I am especially happy that the basic idea seems plausible to you, and am now very confident that in the course of time it will be worked out in a way that is useable in all respects, no matter how imperfect it may be at present.
I am very ashamed about the dreadful “k”, and immediately wrote to the printers; I hope it can still be changed. Many thanks—the worst of it is the ironclad consistency with which I disfigured this hallowed name in five places; it would have been terribly distressing to me.
Thank you very much for kindly sending me your lecture,3 which I had already read with the greatest interest several days earlier. I was especially captivated by the dramatic force with which you sketch the status of the theory of relativity and the quantum theory—in the third section—and with the way you pick out the key difficulty and make it comprehensible without formulas. Just this difficulty concerning the energy unfortunately still persists, quite unimpaired.
If I did not answer your card, which gave me so much pleasure, at once, it was because I wanted to send along at least a little something that was new. Enclosed are the results for the Stark Effect in H. It seems that the intensities come out completely right. The assumption on which it is based is that the electrical charge density is given by the square of the wave function, and that the normalization integral has the same value for all the individual proper vibrations that belong to one coarse Balmer level. I cannot yet describe the numbers I am sending you as incontestable because the calculation is very involved and I have not yet checked everything again. In any case Epstein’s formula for the splitting comes out completely unaltered (as I already said at the end of my “Second Paper”); also the “Selection Rule for the azimuthal quantum number”. Moreover, the “exclusion of zero for the equatorial quantum number” also comes out quite automatically—there is no proper vibration that would correspond to the quantum orbit that collides with the nucleus. It is also very gratifying that although the three unobserved components at relative distances of 5, 6, and 8, are not actually “forbidden” theoretically, they receive an intensity that is 80 to 700 times smaller than that of the weakest observed component, so that their non-appearance becomes very understandable.
I am now calculating Hα, Hβ, Hγ. The calculations are unfortunately terribly difficult to see through and I cannot manage to bring them into a simpler form.
With best compliments and greetings I remain, dear Professor, always