Angel "Java" Lopez en Blog

20 de Julio, 2016

Publicado el 20 de Julio, 2016, 13:52

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Sigo leyendo y comentado el escrito de Max Born:

By consideration of known examples discovered by guesswork, Heisenberg found this rule and applied it with success to simple examples such as the harmonic and anharmonic oscillator. This was in the summer 1925. Heisenberg, suffering from a severe attack of hay fever, took leave of  absence for a course of treatment at the seaside and handed over his paper to me for publication, if I thought I could do anything about it.

Es un clásico de la historia de la ciencia, esa "escapada" de Heisenberg, a Heligoland, por su ataque de fiebre de heno. Vean que Born, igual que Dirac, ve el trabajo de Heisenberg más orientado al tema de ir armando fórmulas que concuerden con los experimentos.

The significance of the idea was immediately clear to me, and I sent the manuscript to the publisher.34 Heisenberg's rule of multiplication left me no peace, and after a week of intensive thought and trial, I suddenly remembered an algebraic theory that I had learned from my teacher, Rosanes, in Breslau. Such quadratic arrays are quite familiar to  mathematicians and are called matrices, in association with a definite rule of multiplication. I applied this rule to Heisenberg's quantum condition and found that it agreed for the diagonal elements. It was easy to guess what the remaining elements must be, namely, null; and immediately there stood before me the strange formula

qp — pq = ih

This meant that the coordinates q and momenta p are not to be represented by the values of numbers but by symbols whose product depends on the order of multiplication - which do not "commute", as we say. My excitement over this result was like that of the mariner who, after long voyaging, sees the desired land from afar, and my only regret was that Heisenberg was not with me. I was convinced from the first that we had stumbled on the truth. Yet again a large part was only guesswork, in particular the vanishing of the non-diagonal elements in the foregoing  expression. For this problem, I secured the collaboration of my pupil Pascual Jordan, and in a few days we succeeded in showing that I had guessed correctly. The joint paper written by Jordan and myself contains the most important principles of quantum mechanics,  ncluding its extension to electrodynamics...

Tanto el "paper" de Heisenberg como el de Born/Jordan, lo podemos encontrar en el excelente Sources of Quantum Mechanics, de van Der Waerden.

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Angel "Java" Lopez

Por ajlopez, en: Ciencia