A Man of Science and Engineering in Troubled Times Wandering in the Late Qing Dynasty

Chapter 697 Mysterious Lover
Heisenberg and Pauli were watching the recently released "The Gold Rush", which was Chaplin's favorite movie. It was a pure comedy and looked light-hearted and joyful.

"Chaplin's films are getting better and better," Heisenberg commented.

"Yeah, no wonder a few of my friends want to go to California to join the film industry," Pauli said.

Heisenberg said, "Well, do you still feel like you can be a comedian now?"

Pauli smiled and said, "I'd better just study quantum physics."

In the evening, Pauli treated Heisenberg to a farewell dinner.

"Congratulations on achieving another outstanding achievement." It is rare for Pauli to praise someone so much.

"I kind of regret not having studied more mathematics," Heisenberg said. "Matrices are so complicated!"

"I have studied your article carefully, and I always have a feeling that electrons no longer seem to move in orbit," said Pauli.

"I feel the same way, and there is no way of knowing what the electron does during the transition," Heisenberg said.

“More than that,” Pauli said, “I am thinking this way. There is no way to know what is happening to an atom or any other quantum entity when no measurement is made on the particle. You can make one measurement and it shows that the atom is in one quantum state, and then you can make another measurement and it shows that it is in another quantum state. But you cannot tell what is really happening to the atom between the two measurements.”

Pauli's physics ability was quite strong, and his ideas at this time already had a bit of the flavor of the uncertainty principle.

Heisenberg had no such idea yet, so he said: "Your statement is too much like pure ancient Greek philosophical speculation. If there is no one there to listen, will a tree fall in the forest and make a sound?"

Pauli took a sip of coffee and said, "The key is how to listen."

Heisenberg deflected the philosophical question and asked, "What about the numbers of molecules in the atomic field that you study?"

Pauli put down his coffee: "Only a few days ago, I felt that in order to complete the theory of energy levels, I would have to introduce quarters and eighths, until finally the whole quantum theory turned into a pile of garbage under my deft hands.

"But I don't think so now. Maybe we just need to introduce one more quantum number according to the spin theory proposed by Mr. Li Yu."

Heisenberg said, "You mean there are two different identical particles of the electron?"

"Yes, they represent different amounts of spin," Pauli said. "In 'The Gold Diggers', Mr. Chaplin was able to marry a beautiful woman, and the electron shouldn't be so lonely."

"Is it possible to solve the anomalous Zeeman effect?" Heisenberg's physics intuition was also good.

Pauli said confidently: "I will write a paper in a week, just wait and see."

Heisenberg said, "Send it to me as soon as possible."

Pauli joked, "You should study matrices first. Even I can understand them! And you have achieved so many results without understanding them."

Heisenberg said: "Let Born and Jordan do the mathematical stuff."

"What do you think of that result?" Pauli asked.

Heisenberg shook his head. "No clue."

Born and Jordan used the matrix method to calculate:

PQ-QP=h/(2πi)
This relationship is so important that it is called the basic equation of matrix mechanics and is engraved on Born's tombstone. Born always felt that this was his most important achievement.

This relationship is important for the entirety of quantum mechanics: if the value of h is zero, then the equations simplify to the formula of classical Newtonian mechanics, namely PQ=QP.

As for the paper of the great Pauli, it is naturally the famous "Pauli incompatibility".

Without his work, which completed the four quantum numbers of the electron theory, Schrödinger would not have been able to derive the wave equation.

Because to study electrons, four quantum numbers are needed:

The first is the principal quantum number that represents the energy level of the electron;

Then there can be multiple orbitals for the same energy level, which is the angular momentum quantum number that represents the shape of the orbital (later developed into electron cloud theory);

The third is the magnetic quantum number representing the orbital direction.

The last one is the Pauli-completed spin quantum number, and the Pauli incompatibility is reflected here.

The great god Pao also explained why the so-called outermost electrons exist and why there are rich and colorful chemical reactions.

It can also explain why matter cannot be infinitely compressed, because there is an "electron degenerate state". Astrophysicists can use this to understand white dwarfs. (As for neutron stars, it's not time yet.)
In short, Pauli's contribution to the new quantum era is revolutionary.

-

Zurich Switzerland.

Although Einstein created his miracle year here and Zurich has some remarkable achievements in science, it is undoubtedly not a very good center for scientific research.

There are two famous universities in Zurich, ETH Zurich and the University of Zurich. ETH Zurich is more familiar to everyone because it is the alma mater of Einstein. The name "Federation" means that it was established by Switzerland in the name of the country and has more sufficient funding.

As for the University of Zurich, it is a state-run university and is much less famous. In the past half century, it was probably only during Clausius' tenure, but he was also working at the Swiss Federal Institute of Technology at the time.

Einstein and Laue also served as professors here for a short period of time, but left soon after.

Since Laue left, the professorship of theoretical physics at the University of Zurich has been vacant for ten years. So there is no need to say much about the scientific research results.

In recent years, the University of Zurich finally had a professor of theoretical physics. The physics faculty unanimously recommended him, saying that his research "involves the fields of mechanics, optics, capillaries, conductivity, magnetism, radioactivity, gravitational theory and acoustics." - Except for the quantum field.

There was even a recommendation letter that emphasized that "he had a good wife."

The professor's name is Schrödinger, also known as Xue Shen.

Unfortunately, since becoming a professor, Schrödinger's health has not been very good and he has mild tuberculosis.

In the 20s there was no cure for tuberculosis, and the only medical solution was rest, preferably at high altitude.

Switzerland has just the right conditions - there are many mountains. As for the principle of this treatment, it may be that high altitude helps the body produce red blood cells, which are believed to fight infection.

The great Heisenberg was recuperating from hay fever, and the great Schrödinger was recuperating from tuberculosis. In any case, they were both on vacation.

But Schrödinger was not as free as Heisenberg, after all, he was a professor.

University professors at this time were different from those in later generations. They had to take on a lot of teaching work. Professors such as Planck, Einstein, Laue, and Bragg had to teach many classes every week.

That's why Li Yu didn't want to be a university professor now, and he would rather be a visiting professor and give lectures when he had time. Bohr had more time because he had a special research institute, where he could train graduate students.

Schrödinger had a heavy teaching load at the University of Zurich, teaching 11 hours a week. In the st century, many university lecturers would not have that much teaching time.

The key point is that Mr. Xue has very broad interests and covers a wide range of subjects. The reasons why those physics teachers recommended him are not groundless.

During this time, Schrödinger was studying color vision in biology and had a strong interest in philosophy. He was somewhat distracted from his studies until Professor Debye of his neighboring school, the Swiss Federal Institute of Technology, invited Schrödinger to attend a seminar.

This is a regular, informal academic seminar hosted alternately by the Swiss Federal Institute of Technology and the University of Zurich. Not many people attend, only about 10 to 20 people each time.

Debye later won the Nobel Prize in Chemistry and was included in the photo of the Fifth Solvay Conference.

Two weeks ago, Debye informed Schrödinger and asked him to talk about the de Broglie matter wave paper which had been very popular in the Annals of Physics at the conference.

This task is naturally not difficult for Mr. Xue, who is very good at mathematics.

At the seminar, Schrödinger spoke eloquently:

"Mr. de Broglie's paper is very forward-looking and philosophical. He cleverly linked particles and waves together, proving that waves are particles and particles are waves. He also explained why electrons can only be in certain orbits, which is very consistent with the quantization rules of Bohr and Sommerfeld.

"Although his theory sometimes results in superluminal wave speeds when calculating wave speeds, these problems should be corrected theoretically in the future."

Schrödinger's understanding of this paper is still very accurate.

After he finished speaking, Debye said to him: "Thank you for your wonderful explanation."

Schrödinger said lightly: "Although the content of the paper is very profound, it is not that difficult to understand."

Debye suddenly asked a question: "I didn't hear it just now. Did de Broglie write about the wave equation of matter waves in his paper?"

Schrödinger said: "No, it is very difficult."

Debye commented casually: "If this is the case, de Broglie's paper is indeed incomplete. Professor Sommerfeld said that to treat waves correctly, one must have a wave equation."

"The wave equation for matter waves?"

Everyone else present thought it was nothing special, but Schrödinger was the only one who paid attention. He remembered the words silently and decided to give it a try.

However, the boss did not come up with the Schrödinger equation all at once. His first thought was to ignore de Broglie's work and try to find a wave equation himself, as long as it could describe the electron fluctuations of the simplest atom, the hydrogen atom.

Since it describes particles with mass such as electrons, it must be the matter wave equation.

Xue quickly derived an equation that took into account the effects of special relativity. Unfortunately, the equation was wrong.

Schrödinger was a little confused and wrote several letters to Einstein, Bohr, Li Yu and others to ask for advice.

As for him? Haha, he's going out for some fun with his lover first!

-

When Li Yu saw the letter, he was preparing to go to Copenhagen as Bohr had agreed. He took a closer look at the letter and read:

"A few days ago I read with the greatest interest the original paper of de Broglie, which I have at last got hold of. From this the future work appears to me more clearly than ever before.

“I even found some connection between de Broglie’s ideas and some papers I published two years ago. But obviously, de Broglie’s thoughts in his grand theory are much more important than my understated statements, and I didn’t know what use those ideas would be at the beginning.

"At this time, when seeking to deepen the study of matter waves, I encountered the following difficulties..."

Li Yu knew after reading it that Schrödinger had not yet started to use his power, but had only tried it briefly, so he replied briefly:

"Yesterday I just read an article about spin by a scholar named Pauli. If you want to derive the wave equation of electrons, you can't ignore this important intrinsic property. Mr. Schrödinger can read that article first."

Schrödinger, who received several replies, was dating his lover.

The lover of Master Xue is also an existence that cannot be ignored in the history of science. She is also very mysterious and no one knows who she is even after a hundred years.

In fact, most biographies of scientists rarely mention the scientists’ gossip stories. Schrödinger and Einstein are quite special.

Several of Schrödinger's colleagues, such as the famous mathematician Weyl, knew that Schrödinger got his inspiration while dating his mysterious lover and came up with the wave equation that shocked the entire physics community.

Many places still retain the "tradition" of Europe that has been around for hundreds of years: married people like to have affairs with others, and this is even considered normal and nothing to be surprised about.

In Schrödinger's circle, his wife Anne had already been having an affair with Weyl...

Weyl's wife was also having an affair with another physicist, Schell, who was a student of Debye and later became the head of the physics department at the Federal Institute of Technology.

Schrödinger must be playing his own game.

It’s a mess anyway!
But it was during the period when he was accompanied by his mysterious lover that Schrödinger produced six papers, which later became wave mechanics.

Schrödinger had the habit of keeping a diary, but unfortunately, for some reason, the volume related to his lover was lost.

He also mentioned "a young female friend" in the preface to his earlier collection of papers on Wave Mechanics.

In short, Schrödinger had a lover in one hand and a paper in the other, and he was good at both.

After reading the reply from Li Yu and others, he decided to give up the research on relativistic hydrogen equations and turn to basic work.

Starting from the wave equation of classical mechanics, Schrödinger used the relationship discovered by de Broglie to convert wavelength into momentum, thereby deriving a wave equation for electrons.

Of course, it sounds easy, but the process actually takes several months.

The wave function we usually talk about is a solution to the wave equation. ——Those who have studied advanced mathematics know that the solution to many differential equations is a function.

The Schrödinger equation is a differential equation that describes matter waves.

Given the boundary conditions, the wave function of a particle at time T can be calculated.

It’s enough to know these basics.

At this point, de Broglie, Heisenberg, and Schrödinger had each completed their own theories, and the conditions for touching the heart of quantum mechanics were in place.

The speed is really fast.