Dirac, who had just then been intensely involved with working out the foundations of Heisenberg's matrix mechanics, immediately understood that these conditions could be met if,, and are " matrices ", with the implication that the wave function has " multiple components ".
42.
It is also said that Heisenberg had consulted Hilbert about his matrix mechanics, and Hilbert observed that his own experience with infinite-dimensional matrices had derived from differential equations, advice which Heisenberg ignored, missing the opportunity to unify the theory as Weyl and Dirac did a few years later.
43.
Although Schr�dinger himself after a year proved the equivalence of his wave-mechanics and Heisenberg's matrix mechanics, the reconciliation of the two approaches and their modern abstraction as motions in Hilbert space is generally attributed to Paul Dirac, who wrote a lucid account in his 1930 classic The Principles of Quantum Mechanics.
44.
Heisenberg's matrix mechanics formulation was based on algebras of infinite matrices, a very radical formulation in light of the mathematics of classical physics, although he started from the index-terminology of the experimentalists of that time, not even aware that his " index-schemes " were matrices, as Born soon pointed out to him.
45.
In the first paper of the trilogy which launched the matrix mechanics formulation of quantum theory in 1925, Werner Heisenberg, a former student of Sommerfeld, working with Max Born at the University of G�ttingen, used the work of H�nl, Kronig, and Goudsmit, referring to it as the " Goudsmit-Kronig-H�nl " formula .
46.
This type of rule differentiates matrix mechanics from the kind of physics familiar in everyday life because the important values are where ( in what energy state or " orbital " ) the electron begins and in what energy state it ends, not what the electron is doing while in one or another state.
47.
One aspect, the idea of modelling atomic behaviour under incident electromagnetic radiation using " virtual oscillators " at the absorption and emission frequencies, rather than the ( different ) apparent frequencies of the Bohr orbits, significantly led Heisenberg and Kramers to explore mathematics that strongly inspired the subsequent development of matrix mechanics, the first form of modern quantum mechanics.
48.
A follow-on paper was submitted for publication before the end of the year by all three authors . ( A brief review of Born's role in the development of the matrix mechanics formulation of quantum mechanics along with a discussion of the key formula involving the non-commutivity of the probability amplitudes can be found in an article by Jeremy Bernstein.
49.
A good example is the famous paper by . ( P . Jordan was especially acquainted with the literature on light quanta and made seminal contributions to QFT . ) The basic idea was that in QFT the electromagnetic field should be represented by matrices in the same way that position and momentum were represented in QM by matrices ( matrix mechanics oscillator operators ).
50.
The work that was done in the past seems passe to us today but that's because we've managed to rewrite the teleology of things so it becomes damned near inevitable that someone would say, " gosh, matrix mechanics would be a useful way of thinking about quantum behavior ! " In reality it was no easier then than it is now to do something truly original.
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