Heisenberg Models and the Rise of Matrix Mechanics

Zihad Hossain
7 min readDec 6, 2020

German physicist Werner Heisenberg was born on December 5, 1901. Max Planck and Einstein co-founded Quantum Theory, which was extensively worked on by Niels Bohr. But Bohr’s atomic model, built using quanta theory, has problems with the trajectory of electrons. Matrix mechanics was born in Heisenberg’s hands to get rid of that problem. Quantum theory is quickly transformed into quantum mechanics. Heisenberg has become famous for his theory of uncertainty. But if matrix mechanics was not born in his hands, who knows how many more years it would have taken to establish quantum mechanics? On the birthday of this famous scientist, there was a tribute from science thinkers. The detailed story of his matrix mechanics is discussed with.

Werner Heisenberg

What does an electron do in the interval between moving from one orbit to another, and where does it reside?

No one has been able to answer this question since the advent of The Broglie. While Broglie is thinking about Bohr’s unresolved problems, another young scientist is looking for answers. In particular, the German young man wondered why Maxwell’s electromagnetic theory did not apply to electron-charged particles. His name is Werner Carl Heisenberg. In German pronunciation his name is Werner Heisenberg.

1925 Heisenberg was only 24 at the time. At that age he devoted himself to quantum theory. Suddenly he had a fever. The famous scientist Max Born is his teacher. He advised Heisenberg to change the air for a while. Following the guru’s advice, he went to an island in the northern ocean. But whose mind is engrossed in Bohr’s atomic model, how can he get out of it! The same thought in his head the electron, why is he thumbing his finger at Maxwell’s theory? What is the quality of an electron that will not let you know what it looks like during a quantum jump?

Heisenberg did not just visit the island. There is a good opportunity to think. Heisenberg once thought that it was wrong to look for the character of an electron during a quantum jump while playing with thoughts and numbers. In fact, the question has no meaning.

If the question is standing on the chest of the round earth, where is the end of the earth? This question is irrelevant. Similarly, the question arises as to where the electrons are in the midst of the quantum leap from one energy level to another energy level. There is no such thing as the direction of the electron that came to Heisenberg’s head. Electrons can only be seen from one position to another. They have no place in between. In fact the direction of the electron cannot be drawn or imagined. Only locations can be identified. This can be compared to chess coats and guts. Any chess piece can be taken to a specific room according to the rules. However, it has nothing to do with playing chess in any way. In other words, the opponents and the judges will see from which house the chess piece is being taken. But when it was taken, it was rolled up, or it was rubbed on the coat, or it was lifted by hand and kept in that room no one pays attention to it. These have nothing to do with playing chess. So no one bothers about this issue. Heisenberg thought the same thing happened when the energy levels of electrons changed.

Whether the electrons are going into orbit exactly according to the quantum conditions is a matter of concern to the scientists. There is no need to know what the electron did in the process of moving from one energy level to another.

Suppose an electron absorbs energy and moves from the first energy level to the third energy level. But the unauthorized orbits in the middle cannot have electrons. So electrons are not supposed to be seen in those orbits. If seen, it would violate the quantum condition. If the conditions were violated, the theory itself would be threatened. So he is not supposed to be seen anywhere in the middle. Of course there is also a permitted orbit between the first and third energy levels to meet a quantum condition. That is the second orbit. Isn’t a glimpse of electrons supposed to be seen in that orbit?

The orbits of electrons are not in the same plane. The second orbit may not fall in front of the electron while going from the first to the third orbit. But what if it falls?

Even then, it is not possible to see that electron in the second orbit. This is because electrons absorb light of a certain energy or frequency and make quantum jump from its orbit. The light of that particular energy determines where the next destination of the electron will be. Electrons will reach directly in that orbit. He will not be able to appear anywhere in between or in any approved orbit. Then the principle of quantum energy exploitation will be violated. So only the position of the electron before and after the quantum jump can be identified, electrons will appear in those two positions, but there will be no electrons anywhere in between.

June 1922. The University of Göttingen invited Bohr to the theory of relativity, David Hilbert. Bohr gave a series of lectures from 12 June to 22 June. The topic of the lecture was the details of the Bohr model. All the physicists, researchers, students of Göttingen are the main listeners of that lecture. Sommerfeld is from the University of Munich. With his two students. The two students are two famous quantum theorists of the future — Wolfgang Pauli and Warner Heisenberg. Bohr’s speech struck a chord with both of them. But Heisenberg did not leave Bohr to question. But Bohr did not have the answer to that question then. Heisenberg later gave birth to quantum mechanics in search of the answer to that question.

In 1920, Heisenberg came to do his PhD under Sommerfeld. And began research on the internal affairs of the atom. Heisenberg tried to explain the heterogeneous Zeeman effect. In doing so, he sat down using a half-quantum number. Half-quantum quantum numbers contradict the principles of quantum theory. So Sommerfeld dismissed that.

Sommerfeld chose a subject for Heisenberg for his doctorate. That is the problem of fluid dynamics. Heisenberg solved it in his own way. That was in 1923. But before the invention of the computer, scientists could not be sure whether it was right. However, after the discovery of the computer in 1952, scientists verified that result — Heisenberg was 100% correct.

In 1923, Heisenberg moved to Göttingen. To do research to Max Burn. In April 1925, he joined Göttingen as an assistant professor. That’s when he started calculating the intensity of the hydrogen spectrum. But he soon realized that this was not possible with conventional mathematics. In fact, there was a flaw in the Bohr model. The Bohr model is based on the hydrogen atom. Going to explain the structure of the hydrogen atom means that inevitably the hydrogen spectrum moves there. This is probably why Heisenberg wanted to calculate the intensity of the hydrogen spectrum.

The light radiates only when the electron jumps from a high energy level to a low energy level. Electrons move from one energy level to another, but in the middle of moving from one position to another, what they do is not found. But the position before and after the jump can be easily found.

I am talking about a simple object. Suppose, the object goes straight from point A to point B. A straight line can be drawn for the object from A to B. A straight line is a long straight line with many points in a row. The object will touch every point on the straight line AB as it moves from point A to point B. So a straight line can be found at each point. Multiplying the two positions of the object from both sides as vector geometry gives the same result. That is: AB = BA. If the object goes in a curve without going in a straight line, we can still write AB = BA. When the path is curved, the object touches every point of the AB curve as it moves. At a given time the object will be at any one point on that curve.

However, this calculation will not work in the case of electrons. Which way the electron goes from A to B cannot be calculated. Because no one can tell whether the path of the electron is a straight line or a curve. Altogether the electrons do not stay at any other point on their way from A to B. Only A and B positions should be brought as. It is not possible to calculate any other position. AB = BA will not be then. For electrons, A and B depend on different quantum numbers. They cannot be multiplied by simple algebraic or geometric rules.

No one has heard of such mathematics before. So many were shocked to see Heisenberg’s equation. Heisenberg himself was looking for an example. That example can be given with the help of this mathematics. He noticed with astonishment that the equation of oddly rhythmic oscillations (not simple rhythmic oscillations) could be explained with his new mathematics.

Soon after, Heisenberg fell ill and, on Bern’s advice, went on holiday to the island. While there, Heisenberg got two solutions. Bohr discovered the method by which all the terms of quantum theory could be written with the help of his mathematics. And with the help of new mathematics, he also invented a mathematical method so that the conservation of energy is not violated. Immediately the ancient quantum theory advanced on the path of quantum mechanics.