Ahora bien, Heisenberg y Schrodinger siguieron distintos métodos para el mismo tema:
Heisenberg and Schrodinger gave us two forms of quantum mechanics, which were soon found to be equivalent. They provided two pictures, with a certain mathematical transformation connecting them.
Pero Dirac también tenía algo para aportar:
I joined in the early work on quantum mechanics, following the procedure based on mathematics, with a very abstract point of view. I took the noncommutative algebra which was suggested by Heisenberg's matrices as the main feature for a new dynamics, and examined how classical dynamics could be adapted to fit in with it. Other people were working on the subject from various points of view, and we all obtained equivalent results, at about the same time.
Como menciona, lo importante para él fue la no conmutatividad que exhibía el modelo matemático.
I would like to mention that I found the best ideas usually came, not when one was actively striving for them, but when one was in a more relaxed state. Professor Bethe has told us how he got ideas on railway trains and often worked them out before the end of the journey. It was not like that with me. I used to take long solitary walks on Sundays, during which I tended to review the current situation in a leisurely way. Such occasions often proved fruitful, even though (or perhaps because) the primary purpose of the walk was relaxation and not research.
It was on one of these occasions that the possibility occurred to me of a connection between
commutators and Poisson brackets. I did not then know very well what a Poisson bracket was, so was very uncertain of the connection. On getting home I found I did not have any book explaining Poisson brackets, so I had to wait impatiently for the libraries to open the following morning before I could verify the idea.
Ver Dirac revisando el trabajo de Heisenberg.
Angel "Java" Lopez