The most famous quantum equation was published in 1926 on just two pages. What does she describe and how did Schrödinger think of her?
The Austrian scientist Erwin Schrödinger was a scientific wizard. Arnold Sommerfeld, one of the pioneers of quantum theory, previously referred to the equation that made Schrödinger famous as "the most wonderful discovery of all the wonderful discoveries of the twentieth century". When Max Planck, one of the first to recognize the quantum nature of light, held Schrödinger's second paper in his hand, he was passionately quoted as saying: "I read your words like a curious and enthusiastic child trying to decipher puzzles that have troubled me for a long time and I fade from the beauty that my eyes reveal. I must delve into your ideas to grasp them in full."
Years later, Richard Feynman, who won the Nobel Prize for formulating the quantum electromagnetic theory, said of Schrödinger: "Where did he get it (the Schrödinger equation)? From nowhere. It cannot be extracted from anywhere. It came from Schrödinger's mind, while he was trying understand the experimental observations of the real world". Like Feynman, historians believe that Schrödinger never explained how the most famous quantum equation came to his mind but it is certainly possible to guess what ideas led to the formulation of the revolutionary paper in 1926.
Schrödinger was inspired by the doctoral project of a young researcher named Louis de Bruy. Following the photoelectric effect described by Albert Einstein, de Broy assumed that the particles of matter also have wave properties. The controversial thesis was sent to Schrödinger who at first did not even bother to address it. To De Bruy's surprise, it was Albert Einstein who was enthusiastic about the paper and ignited the idea among the scientific community. A few months later the physicist Peter DeBay asked Schmertinger to give a lecture on de Bruy's thesis in Zurich. When the lecture was over, Debay turned to Schrödinger and said: "If what you say is true, meaning that particles do behave as waves, there must be a wave equation that describes them, why don't you try to find it?" And indeed it was.
Schrödinger, who used to go on vacations without his wife (and even had affairs with other women), decided to go far alone this time to solve the problem. At the end of the vacation he held the paper written on one page on both sides detailing the wave equation now known as the Schrödinger equation. To explain the short article prior knowledge of analytical mechanics is required and in truth some would argue that Schrödinger did not really develop the equation from basic principles, but assumed it to be true. So what is the Schrödinger equation? De Broy's particle-wave duality together with the fact that plane light waves advance in time proportional to energy led Schrödinger to write down the following equation:
The equation consists of two parts: the right-hand side multiplies the energy of the particle (equivalent to the expression H, the Hamiltonian) with its wave function (marked by the Greek letter pesei) and the left-hand side evaluates the time derivative of the wave function. In other words, the change in time of the wave function is equal to the energy of the particle. Before we continue I just want to emphasize how elegant this equation is. It is the energy of the particle that forces the wave function to change in time. If we replace H with some numerical value, the solution to this equation will resemble a plane wave function. In quantum mechanics H is not a number, it is an operator. An operator, as its name implies, performs an operation on the object on which it operates. In our case, H acts on the Pessie wave function. If Pesei describes a physical state of a particle with a defined energy, H will be replaced by the energy belonging to Pesei. If the wave function describes a superposition of energy states (that is, the particle can be in several different energy states, each with a certain probability), mathematically Pesci will be written as a sum of specified energy states. In this case H will act on each of the energy states separately and will be replaced by its value as the conjugate factor for each state accordingly. H's operation on the Pesei state dictates at every moment how it changes.
Sometimes the Schrödinger equation looks like this:
This equation is in total a different writing of the energy operator H with the help of its components - each particle has kinetic energy and potential energy (marked by the letter V). From similar considerations that led physicists to equate electromagnetic plane waves with particle wave functions, the kinetic term can be replaced by a second derivative of the space When writing the Hamiltonian like this, the wave equation is fully revealed For a moment and to make a technical note - a real wave equation contains a second derivative in both space and time, unlike the Schrödinger equation which involves a first derivative in time and a second derivative in space. At the same time, the use of the term wave function to describe the solution to the Schrödinger equation is not mathematically incorrect because the solution does look like a spatial wave ( This is thanks to the imaginary member i).
The function of the Schrödinger equation is to calculate the Pessian wave function at each instant. The absolute value of the squared wave function describes the probability of the particle being in a certain position at some time. The Schrödinger equation was proven to be effective in predicting the behavior of particles in nature and was revalidated when it was able to accurately describe the structure of the hydrogen atom. Despite the many successes of the Schrödinger equation, there are quite a few limitations. The equation is not a relativistic equation (the equation refers differently to time and space, and the energy H described in the last equation is not relativistic) in addition it is not able to describe more than a single particle. Years later, Klein, Gordon and Dirac formulated relativistic equations similar to the Schrödinger equation and field theory solved the mystery of describing multi-particle systems. The Schrödinger equation is considered a cornerstone of quantum mechanics and is still used today. Schrödinger made many contributions in science, but there is no doubt that the sharp intuition of the genius physicist appeared in its greatness in one equation that changed our perceptions of the world and the laws of nature.
Each week I will dedicate an article to an idea or a common concept in modern physics. If you have suggestions or requests for this corner, you are welcome to contact me at the email address: Noamphysics@gmail.com
9 תגובות
Some nonsense in one place
The Schridinger equation is flawed since he did not write it according to the discovery of these researches fraudulently and this equation was known to me before him. In the article it is noted that there is no explanation of how he came up with it. And since I came up with it before him then to prove it the book is the form in which he supposedly came up with it. A. He is not What he did was that there were other scientists who were looking for the beacon and many options came up. What he did was that he collected all the options that the scientists came up with and with their help all the options that turned out to be incorrect. It turned out that one of his options came to mind because they made a mistake in the calculations and reached a dead end that there were no more options. And it remained A really simple option that has not been tried because it appears to be illogical and unacceptable and in short the great scientists searched the sky and it was in front of their eyes and meaningless and that Dinger who knew that there was no possibility that could be acceptable then proposed the equation and put his name and honor on it that it is correct only for the reason that it cannot be proven to be incorrect and the discovery of its incorrectness It is equivalent to the solution, and since he understood this, he bet with confidence that this is the correct beacon. But it is clear that it was achieved fraudulently, even in this trial and error trial and error that giant scientists tried to negate equations that did not match, and as mentioned, he made no effort at all, and this is really cheating. And I thought about the fact that he proposed the equation whose negation is like solving An enigma cannot be solved and if you can deny the solution then you have solved the enigma. I hope that as a result of these words the mite will be removed from him and the scientists who have solved the possibilities will be awarded the possibilities they have excluded and exhausted all the possibilities and for that they deserve the prize. A huge thought in which you check options that are at a high altitude and it is difficult to easily believe the solution. Therefore, some reject the equation, for whom this equation was initially ruled out as incapable and completely correct
The cat is in the second part
It creates the effect and then disappears
This is one of your best articles!
How nice that you also included the mathematical equation and not only explained the idea in words.
Erwin with his psi can do
Calculations quite a few.
But one thing has not been seen:
Just what does psi really mean?
Science must be well understood and explained.
I didn't understand anything from your explanation. Too bad. For the sake of transparency, I am a doctoral student in biology
Excellent explanation, amazing in its simplicity, well done
What about Schrödinger's cat? How is this related?
Schrödinger received the equation from a traveler while he found it written in a textbook on quantum mechanics and Schrödinger equations. This is the only way to sometimes progress in physics