D O C U M E N T 2 4 7 A P R I L 1 9 2 6 2 6 1 matrix of the energy in V, one can calculate the averages and assign these again to the individual states.[4] Naturally, there is no doubt that the higher powers … all have the right thermodynamically calculable val- ues. However, the probability that for a state all the energy will be empirically found in V is fully defined by these averages, hence comes out correctly, when the averages are correct it seems to me impossible to doubt that one really would ar- rive at the formula in this way. Consequently, it seems to me that the relation of matrix theory to this problem certainly can be clearly indicated. Two more questions arise: 1) How can the probability defined in the above sense really be calculated from matrix theory without one first having to know the infinitely many averages ? This is a purely mathematical question, however and if one is convinced that one would arrive at the right result, if the above-described path were practicable, one will not consider this question to be of particular interest at present. 2) Can one expect to obtain (as in the classical theory) from a generalized and more advanced theory containing the results of matrix theory for each individual state a temporally variable number that represents the energy in V ? I do not dare to try to answer this question now, although I would like to believe that one must have this expectation or must look for such a generalization of the physical theory. Thus, in brief: The empirical function = energy in V for a particular state cannot be calculated according to the matrix theory. Yet can be calculated and one gets the right result, definitely for n = 1, 2, and probably for n 2. It remains to be seen whether a more advanced physical theory will make itself theoret- ically definable. The current state of affairs can certainly still be called unsatisfactory but, in my view, it cannot be said that the wave theory treated on the basis of matrices leads here to inconsistencies in any way. It would naturally be very important to me if I were permitted eventually to learn of your opinion on these matters. It is not yet certain whether I am going to be coming to Berlin for a while in the summer. If I should be in Berlin one day, though, I shall not fail to visit you, of course. Surely, at the latest I will be able to introduce myself to you in Düsseldorf.[5] With friendly regards, respectfully and sincerely yours, P. Jordan E E E)2, – ( E E)4, – ( … , E E)4 – ( W V V0¹ -----· - © § E hν ------ = En f t) ( f t)n ( f t) (