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Штирлиц и Матрица
Oct. 2nd, 2011 09:49 amИз нобелевской лекции Макса Штирлица Борна, про открытие матричной механики его ассистентом Гейзенбергом:
"Instead of describing the motion by giving a coordinate as a function of time, x(t), an array of transition amplitudes x_(mn) should be determined. To me the decisive part of his [Heisenberg] work is the demand to determine a rule by which from a given array the array for the square can be found (or, more general, the multiplication rule for such arrays). By observation of known examples solved by guess-work he found this rule and applied it successfully to simple examples such as the harmonic and anharmonic oscillator.
This was in the summer of 1925. Heisenberg, plagued by hay fever took
leave for a course of treatment by the sea and gave me his paper for publication if I thought I could do something with it.
The significance of the idea was at once clear to me and I sent the manuscript to the Zeitschrift für Physik. I could not take my mind off Heisenberg’s multiplication rule, and after a week of intensive thought and trial I suddenly remembered an algebraic theory which I had learned from my teacher, Professor Rosanes, in Breslau. Such square arrays are well known to mathematicians and, in conjunction with a specific rule for multiplication, are called matrices. I applied this rule to Heisenberg’s quantum condition and found that this agreed in the diagonal terms. It was easy to guess what the remaining quantities must be, namely, zero; and at once there stood before me the peculiar formula
pq - qp = h/zni
This meant that coordinates q and momenta p cannot be represented by figure values but by symbols, the product of which depends upon the order of multiplication - they are said to be « non-commuting »."
После недели напряженных размышлений, Борн вспомнил, что когда то он проходил такие таблички и правила их умножения в курсе алгебры, и назывались они матрицами. Похоже на анекдоты про Штирлица:
Мюллер:
- А вы молодец, Штирлиц.
- Служу Советскому Союзу! -
по привычке ответил Штирлиц и подумал:
"Надо было и про фюрера что-то сказать".
"Instead of describing the motion by giving a coordinate as a function of time, x(t), an array of transition amplitudes x_(mn) should be determined. To me the decisive part of his [Heisenberg] work is the demand to determine a rule by which from a given array the array for the square can be found (or, more general, the multiplication rule for such arrays). By observation of known examples solved by guess-work he found this rule and applied it successfully to simple examples such as the harmonic and anharmonic oscillator.
This was in the summer of 1925. Heisenberg, plagued by hay fever took
leave for a course of treatment by the sea and gave me his paper for publication if I thought I could do something with it.
The significance of the idea was at once clear to me and I sent the manuscript to the Zeitschrift für Physik. I could not take my mind off Heisenberg’s multiplication rule, and after a week of intensive thought and trial I suddenly remembered an algebraic theory which I had learned from my teacher, Professor Rosanes, in Breslau. Such square arrays are well known to mathematicians and, in conjunction with a specific rule for multiplication, are called matrices. I applied this rule to Heisenberg’s quantum condition and found that this agreed in the diagonal terms. It was easy to guess what the remaining quantities must be, namely, zero; and at once there stood before me the peculiar formula
pq - qp = h/zni
This meant that coordinates q and momenta p cannot be represented by figure values but by symbols, the product of which depends upon the order of multiplication - they are said to be « non-commuting »."
После недели напряженных размышлений, Борн вспомнил, что когда то он проходил такие таблички и правила их умножения в курсе алгебры, и назывались они матрицами. Похоже на анекдоты про Штирлица:
Мюллер:
- А вы молодец, Штирлиц.
- Служу Советскому Союзу! -
по привычке ответил Штирлиц и подумал:
"Надо было и про фюрера что-то сказать".
