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The period from 1925 to 1926 was a miracle year of quantum mechanics. in this year, only six months apart, two major theories of quantum mechanics-matrix mechanics and wave mechanics-were born, just like two boulders thrown into the water, setting off great waves. It not only impacted the older generation of physicists, but also inspired the younger generation of vitality.

The two theories have formed two major schools, which involve the whole physics circle in a heated and lasting dispute. Disputes promote the development of theory and open up new ideas. the principles of complementarity, wave function "collapse" and quantum entanglement are born and mature in the debate, and the third generation of newcomers of quantum mechanics are also bred and grown up in this great debate. they become the third echelon of the development of quantum theory, setting off the new and most exciting parts of the theoretical and experimental research of quantum mechanics. As a result, quantum field theory, standard model, particle physics and even cosmology quantum theory have been developed.

Erwin Schrodinger, the founder of quantum mechanics, was also a "teenage wizard". He loved mathematics and was good at it. He not only used mathematics to develop quantum theory, thus creating the world-famous wave dynamics, but also applied mathematics to the study of general relativity, cosmology, meteorology, acoustics, radiology, meson physics, quantum field theory, astrophysics, optics, unified field theory, and even life sciences.

Although Schrodinger has made a lot of achievements, he started late in the study of quantum theory, and his progress is slow and tortuous. Schrodinger was nearly 40 when he founded wave mechanics, while Heisenberg was only 24 when he built matrix mechanics.

Schrodinger started late for a reason. In 1906, Schrodinger entered the University of Vienna and studied theoretical physics from the famous physicist Boltzmann. In less than half a year, Boltzmann committed suicide in Rome, Italy, due to severe depression. Boltzmann's death made the ambitious Schrodinger lose the goal to follow, and he lacked a navigator in his early scientific career.

From 1921 to 1922, physics was on the eve of the great development of quantum mechanics, and many valuable works and papers were published one after another. When attending the 4th Solvay Physics Conference, Schrodinger realized that the study of electrons was the mainstream of the development of physics, but he could not come up with any decent papers. This is a great stimulus to Schrodinger, as he said several years later: "in my scientific career, I have never been able to move forward along a main line, and no result has been able to determine my long-term development direction."... Despite some achievements, no one has ever been in the lead, not secondhand, after agreeing with others, or inspired by refutation. Although sometimes the result of this extension may seem important, it is still a connection. " Schrodinger was 34 years old when he said this.

In the field of modern quantum physics, the peak age at which cutting-edge physics masters became famous was mostly in their twenties, or at most in their early thirties. Einstein was 26 when he proposed the optical quantum theory, 24 when Heisenberg established matrix mechanics, 25 when Dirac proposed the famous equation, 25 when Pauli proposed the incompatibility principle, 30 when born proposed the statistical interpretation of wave function, and 31 when de Broglie proposed wave-particle duality. Schrodinger suddenly realized the crisis, but the 34-year-old has not yet chosen his research direction.

At this time, the University of Zurich is selecting teachers, and after reading Schrodinger's application, the professors' committee commented on him: "Schrodinger has made achievements in mechanics, optics, acoustics, capillarity, electrical conductivity, magnetism, radioactivity, gravitation, and so on." Although he is a generalist, he has "failed to produce eye-catching results in any particular field", and some people even think that "with such broad interests and versatile abilities, it is impossible to make any major discoveries." As it turns out, this claim is premature.

In his first semester at the University of Zurich, Schrodinger taught four hours of analytical mechanics, four hours of electrical theory, two hours of special topics on theoretical physics and an one-hour progress report on physics. In the theoretical physics class, there is also a "deformable body dynamics", it is the opportunity for this lecture, so that he is familiar with the operation of tensor. In addition to teaching, he also has scientific research projects, in addition to continuing the previous topics of relativity, electronics, color, thermodynamics and statistical mechanics, he began to add Bohr's atomic quantum theory. The joint paper of Bohr, Kramer and Slatter, known as BKS, attracted the attention of Schrodinger as soon as it was published. On September 5, 1924, Schrodinger published a discussion of this theory through calculation. From this, it can be seen that Schrodinger is slowly approaching the frontier of atomic quantum theory.

As Schrodinger said of himself, the habit of doing "second-hand" research "inspired by others or refuting others" makes him very good at thinking about things that others have never found before, so as to get what others don't get. In 1924, French physicist Louis de Broglie published a paper on the wave-particle duality of microscopic particles, which was one of the reasons why Schrodinger founded wave dynamics.

While preparing for the course of Molecular Statistics, Schrodinger found a subject worth studying and began to study gas theory from the perspective of quantum theory. In December 1925, he completed his paper on the study of Einstein's Gas Theory. Based on quantum theory, with skillful and exquisite mathematical derivation, accurate and meticulous theoretical analysis, and using the evaluation method of probability statistics, this paper deduces the law of Einstein-Bose gas statistics. This paper became a brilliant debut on the eve of Schrodinger's founding of wave dynamics.

In the winter semester of 1925, Schrodinger was not in good health, and the tasks he could teach were still very heavy. He had five hours of electromagnetic theory classes and two hours of spectral theory classes a week, as well as two hours of topic discussions on electromagnetics, as well as fortnightly, two-hour lectures for the Federal Institute of Technology in Zurich (Eidgen.ssische Technische Hochschule, ETH). This lecture needs to keep up with the development of the frontier topics of physics at that time, and its difficulty can be imagined at the time of the rapid development of modern physics. At this time, de Broglie's paper sparked a heated discussion among the students, and Debye, head of the physics department of ETH, suggested that Schrodinger give a special report on the theory of wave-particle duality for the lecture.

The physics lecture of the Federal Institute of Technology in Zurich has a high reputation and has influenced a new generation of physics. At that time, the third generation of quantum mechanics, such as von Newman and Phyllis Bullock, were listening to the lecture. On November 23 of that year, Schrodinger gave a lecture on de Broglie's thesis at ETH. Maybe the expectations were too high. After the first lecture, Debye was very dissatisfied, but the second time the situation was very different. Brock, a Debye student, later recalled: "Debye said with dissatisfaction that the report was simply 'naive'. As early as when Sommerfeld was a student, he knew what the properties of waves should be and that they should be expressed by an equation. But in another lecture two weeks later, Schrodinger said at the beginning of the class,'my friend Debye suggested that I should come up with a wave equation, and now I have found it!'" Schrodinger's wave dynamics was unveiled in this lecture.

The scene of Schrodinger in the lecture when Schrodinger's wave theory was built, and the time cannot be tested. Schrodinger has a habit of recording at any time, although these notes are classified according to the content and process of the subject, but most of them are not dated.

During the Christmas holiday in 1925, Schrodinger went to Aloza for a holiday. It seems that during this period, his study of wave dynamics has made remarkable progress, and many people think that wave dynamics was born during the holiday.

During his vacation, he wrote to his friend William Wayne: "I am struggling with this theory." If there is one person who knows the beauty of mathematics, it is me. I am quite optimistic about this. Only I can work it out. It is a perfect theory. What I need to do is to add a little detail to make it easier to understand. This is a little-known linear differential equation similar to Bessel and I look forward to publishing it as soon as possible. "

This letter shows that he has not only obtained the wave equation with all eigenvalues under quantitative conditions, but also tried to solve it. Schrodinger's wave equation is in the following form:

At that time, he had not yet separated the component form of the three-dimensional wave equation, and it was impossible to find out how the azimuth and magnetic quantum number appeared in the angular component of the equation, so the theory should not have been finally completed.

With the wave equation, Schrodinger's first step is to separate variables. In the case of single electron spherical symmetry, its potential energy is obtained at first, and three standard differential equations in the case of spherical symmetry are obtained. One of them is called the ray equation, which is the biggest headache for Schrodinger. When he returned to Zurich after the holiday, he stayed behind closed doors to deal with it all day.

On January 11, 1926, he finally found the solution of the equation, which was later called the Colin-Gordon equation (Klein-Gor-don-Equation). To his bewilderment, he found that the solution was obviously inconsistent with the experimental results. It turned out that the problem was that the spin of the electron was not taken into account in the whole theoretical framework, and the spin of the electron had not been discovered at the time. But this solution is perfect for particles with zero spin.

Schrodinger finally finished his thesis on wave dynamics. He sent it twice, and the first article was sent to the Yearbook of Physics, which was received by the magazine's editorial department on January 26, 1926, entitled "quantization of the eigenvalue problem." Four weeks later, he published a second paper on the same topic, and then in less than half a year, he published six papers in a row. Schrodinger's research method is very ingenious. Through the Hamiltonian analogy between mechanics and optics, not only the wave equation is derived, but also the relationship between wave dynamics and geometry is further analyzed. the application of wave equation in single-electron harmonic vibration and diatomic molecule theory is discussed, and the results are consistent with the experimental data.

It is worth mentioning that Schrodinger makes analogies in mechanics and optics in mathematical form, from which he expresses the law of quantum waves. These six papers create a complete framework of wave dynamics and systematically answer all kinds of quantum phenomena known at that time. The authoritative and forward-looking nature of this theory makes it a unique masterpiece in the history of science.

Schrodinger's work shocked the whole physical world and touched Planck, the ancestor of quantum theory. When he read the first paper, he said, he was "as excited as a child who suddenly knew the answer after being haunted by a riddle for a long time." He appreciated the second paper more, calling it "an epoch-making masterpiece".

Einstein also commented: "the ideas revealed in the paper come from a real genius!" Soon Einstein sent another letter: "your mathematical theory under quantum conditions has made decisive progress, and I am sure that Heisenberg and born's (matrix mechanics) method has lost its leading position." Although it was too early for Einstein to say this, he reminded Schrodinger that he would face a challenge of how to deal with another theory that emerged at the same time-matrix mechanics.

Sure enough, the two theories of quantum mechanics collided directly. After Schrodinger completed six papers on wave dynamics equations, he has become a world-famous figure. In 1927, Schrodinger was invited by the German Academy of Sciences to give a lecture on wave dynamics at the Bavarian branch of the German Scientific Society, and Heisenberg, the founder of matrix mechanics of quantum mechanics, was present.

Heisenberg listened patiently as Schrodinger gave his lecture. At the end of the report, Heisenberg finally couldn't bear to stand up. He pointed out that Schrodinger's wave dynamics could not explain some basic physical phenomena, such as Planck's law of radiation, Compton effect, or even the intensity of the characteristic lines of atoms, because they all showed the quantum characteristics of discontinuity, or related to the characteristics of quantum transitions. Under this series of attacks, the moderator of the meeting and Heisenberg's old enemy, Wayne, an experimental physicist at the University of Gottingen, forced Heisenberg to sit down. Without any explanation, Schrodinger broke up the meeting. Later, Heisenberg told his brother Pauli that Wayne "almost threw me out of the house."

From then on, the dispute between the two schools of quantum mechanics began, led by Einstein on one side and Bohr on the other, the interpretation of the theory of quantum mechanics began a heated debate for more than ten years. Quantum mechanics grew up in the debate, from which the third generation of new people of quantum mechanics emerged, such as Wheeler, Von Neumann, Feynman, Bohm, Bell, Aspe and Krausse and so on. Their research results expand the interpretation of the theory of quantum mechanics.

Standing on both sides of the Swedish king are these two contentious opponents, Schrodinger (left) and Heisenberg (right), who co-founded the epoch-making quantum mechanics in 1933. Schrodinger won the Nobel Prize in physics for his contribution to quantum mechanics, along with his controversial opponents, Heisenberg and Dirac, the founders of matrix mechanics.

Source: 365 days in the History of Science, slightly edited by: Wei Fengwen Wu Yi Editor: Zhang Runxin this article comes from the official account of Wechat: Origin Reading (ID:tupydread), author: Wei Fengwen, Wu Yi, Editor: Zhang Runxin

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