Angel "Java" Lopez en Blog

21 de Enero, 2017

Publicado el 21 de Enero, 2017, 13:25

Ya apareció por este blog el tema de grupos y física, en especial, cuántica:

Grupos y Física, por Dirac
Teoría de Grupos y Partículas Elementales
Hermann Weyl, Teoría de Grupos y Teoría Cuántica

Encuentro hoy unos párrafos de Abraham País, en su excelente "Inward bound, of matter and forces in the physical world", en un capítulo dedicado a grupos y la "clásica" mecánica cuántica:

Nearly a year after Heisenberg had considered the theory of one linear oscillator and so discovered quantum mechanics, he had something interesting to say about two identical oscillators symmetrically coupled to each other. The quantum states of this system, he found, separate into two sets, one symmetric, the other anti-symmetric under exchange of the oscillator coordinates. Assuming further that the oscillators carry electric charge, he noted that radiative transitions can occur between states within each set, never between one set and the other. He further conjetural that non-combining sets should likewise exist if the number n of identical particles is larger than two, but had not yet found a proof. He left this problem aside; another question was on his mind. Six weeks later he gave the theory of the hellium spectrum, that bane of the old quantum theory. To Pauli he complianed that his calculations were 'imprecise and incomplete'. It is true that others were able to refine his answer in later years. Nevertheless, his outstanding paper  contains all the basic ingredients used today. The first quantum mechanical application of the Pauli principle is given: two-electron wave functions are antisymmetric for simultaneous exchange of space and spin coordinates. That  principle is the subject of the following section...

Meanwhile in Berlin a young Hungarian chemistry engineer, Jenö Pál (better known since as Eugene Paul) Wigner, had become interested in the n > 2 identical particle problem. He rapidly mastered the case n = 3 (without spin). His method were rather laborious; for example, he had to solve a (reducible) equation of degree six. It would be pretty awful to go on this way to higher n. So, Wigner told me, he went to consult his friend the mathematician Johnny von Neumann. Johnny thought a few moments then told him that he should read certain papers by Frobenius and by Schur which he promised to bring the next day. As a result Wigner's paper on the case n (no spin), was ready soon and was submitted in November 1926. It contains an acknowledment to von Neumann, and also the following phrase: 'There is a  well-developed mathematical theory which one can use here: the theory of transformation groups which are isomorphic with the symmetric group (the group of permutations)'.

Thus did group theory enter quantum mechanics.

El propio Wigner escribió un libro "clásico" "Group Theory and Its Application to the Quantum Mechanics of Atomic Spectra". Y ya mencioné en un post de arriba, al trabajo de Weyl.

Vean cómo el trabajo de Heisenberg fue precursor de la aplicación de grupos. Luego, él mismo se encargaría de introducir las simetrías internas, en el caso protón-neutrón, que inauguraría otra rama de aplicación, la de teoría de grupos en partículas elementales.

Nos leemos!

Angel "Java" Lopez

Por ajlopez, en: Ciencia