Probabilities of the Quantum World (Pt-8)
Summarizing the Masterpiece by Daniel Danin
[To refresh, text in such square brackets is my commentary. Rest of it is a faithful documentation of the most fascinating story ever told of the Quantum Revolution]
[At the end of Part-7, we learned of a new quantum number that had been discovered, of which Schrodinger was unaware of as he was starting his deep dive into developing matter-wave mechanics.]
[We are now entering the most fascinating era. The Quantum description of the atom is taking shape rapidly and there is light at the end of the proverbial tunnel. Things now begin to get a bit complicated. Simple explanations are becoming difficult to find. This part of the story will need you to stick with the narrative and simply follow the story without sometimes understanding it.]
Staying in the spring in the quiet mountain village of Arosa, Erwin Schrodinger tried to avoid any — even scientific — distractions in order to concentrate on the search for the mechanics of the matter waves. He had even heard nothing about the birth of the new quantum number. He was punished for his ignorance, but in a very peculiar way…
To derive a wave equation… this meant that its solution would be graphically represented as waves in the space of the atom. A certain quantity symbolically describing the states of the atom would vary in a wave form from point to point, and from moment to moment. If the equation has been properly derived, its solution will reflect the sequence of the stable states in which the atom does not emit energy and all the transitions between such states when energy is emitted in the form of quanta.
Schrodinger decided to select a not too popular letter of the Greek alphabet for denoting this ‘certain quantity’ which was mathematically clear but physically still rather mysterious: the letter psi.
“A moving particle is nothing else but the foam on the wave radiation forming the matter of the world”
Was it not the waves of Lake Zurich that has whispered these magic words to him? When the wind produced random foamy crests on the surface of the lake that was an indication that the water waves of different wavelengths and different amplitudes had successfully superposed on each other: near the trough they were mutually cancelled out and at the site of the crest were mutually intensified. Why could we not admit that the electrons (and in fact, all microscopic particles of matter) were the packets of interfering matter waves? But then there are no wave-particles having a dual nature! We had to deal only with wave-waves, and everything was continuous — that was the dearest thought of Erwin Schrodinger, his fondest hope.
A true understanding of the physical meaning of ‘psi’ came later — and it was not Schrodinger’s doing. This happened much later when his famous equation had already been well applied in the mechanics of the submicroscopic world.
Schrodinger could not manage to give his theory a proper form because he was unaware of spin. Such was the irony of history: precisely at the moment when the prominent scientist hoped to eliminate all discreteness from the picture of the submicroscopic world, yet another discrete feature appeared in this world — the electron spin. But Schrodinger did not know about this and could not incorporate it in his theory.
Apparently, when he descended from the mountain village of Arosa into the summer Zurich of 1925, he had a first version of his equation with him. He later told Paul Dirac:
“… I immediately applied my method to the motion of the electron in the hydrogen atom, properly taking into account the formulas of the relativity theory for such an electron… The calculated results did not agree with the observational data… I was deeply disappointed, decided that the method was unsuitable and dropped it.”
He dropped it! — at this moment the fate of wave mechanics was hanging by a thread. He assumed that he had ‘properly’ taken into account the relativity theory; but to do that really properly he had to take into account the inherent rotation of the electron, its spin, quite apart from the effect of its enormous velocity.
[There is always something we miss. I am therefore skeptical each time I develop a theory. If the theory agrees with data, I attempt to find situations where it would break. These are called limiting conditions — the ultra simplified situation where one can ‘reason’ the answer out and check whether it matches the theory. If the theory does not agree with the data, I check whether the data is wrong or ‘did I miss something’!]
[As an aside, Paul Dirac was the one who in 1928 derived the relativistic equation for quantum mechanics (which is no less great an achievement than that of Schrodinger).]
Fortunately, Schrodinger’s work was too personal to him and he did not give up! He avoided introducing relativity theory — he simplified the problem and tried to solve it with lower accuracy and immediately the equation yielded results that agreed with experimental data! It was one of those cases of ‘the simpler the better’. By the end of 1925 Schrodinger thus had a wonderfully effective, though not completely accurate, wave equation! Then he started to write a series of papers.
The first was submitted to Annalen der Physik on January 27, 1926. Almost a year had passed since that day unmarked in history when two theorists from Zurich had admitted to each other not understanding the concepts of de Broglie, and arranged a discussion of this thesis. Now one of them had developed the wave mechanics which would soon gladden the hearts of all who felt themselves ‘in a blind alley’.
Amazingly, the gladness was not diminished by the obscurity which still enveloped the psi-waves discovered by Schrodinger.
… To be Continued
[In the next part, we will shift our story to the other theorist who did not understand de Broglie’s work, Werner Heisenberg.]
[Oh ya… for the Medium uninitiated, please leave a couple of “claps” below if you like this and would be interested in the subsequent part(s). Thanks.]