En el anterior post, comentaba que Dirac tenía un ejemplo de aplicación de los dos métodos que proponía, sobre el mismo tema. El ejemplo es el de la mecánica cuántica:
Whether one follows the experimental or the mathematical procedure depends largely on the
subject of study, but not entirely so. It also depends on the man. This is illustrated by the discovery of quantum mechanics.
Two men are involved, Heisenberg and Schrodinger. Heisenberg was working from the experimental basis, using the results of spectroscopy, which by 1925 had accumulated an enormous amount of data. Much of this was not useful, but some was, for example, the relative intensities of the lines of a multiplet. It was Heisenberg's genius that he was able to pick out the important things from the great wealth of information and arrange them in a natural scheme. He was thus led to matrices.
Schrodinger's approach was quite different. He worked from the mathematical basis. He was not well informed about the latest spectroscopic results, like Heisenberg was, but had the idea at the back of his mind that spectral frequencies should be fixed by eigenvalue equations, something like those that fix the frequencies of systems of vibrating springs. He had this idea for a long time, and was eventually able to find the right equation, in an indirect way.
Yo igual mencionaría que el trabajo de Heisenberg también partía de un modelo matemático, el desarrollo en serie de Fourier y aledaños, para sí. basado en los datos experimentales, proponer un salto en ese modelo.
Angel "Java" Lopez