Louis de Broglie believes that not only photons obey this relationship, but all particles obey it. His further De Broglie hypothesis in 1924 shows that every microscopic particle has fluctuation and particle property, which is called wave-particle duality. Electrons also have this property. Electrons are a kind of matter waves, which are called "electron waves". The energy and momentum of an electron respectively determine the frequency and wave number of the matter wave accompanying it. In atoms, bound electrons form standing waves; This means that his rotation frequency can only take some discrete values. These quantized orbits correspond to discrete energy levels. Starting from these ideas, de Broglie copied the energy level of Bohr model.
1925 Zurich, Switzerland holds a physics seminar every two weeks. On one occasion, the organizer peter debye invited Schrodinger to talk about the wave-particle duality of De Broglie in his doctoral thesis. During that time, Schrodinger was studying gas theory. He came into contact with De Broglie's doctoral thesis by reading Einstein's exposition on bose-einstein statistics, and he had a profound understanding in this respect. At the seminar, he expounded the duality of wave and particle incisively and vividly, and everyone listened with relish. Debye pointed out that since particles have volatility, there should be a wave equation that can correctly describe this quantum property. His suggestion gave Schrodinger great inspiration and encouragement, and he began to look for this wave equation. The simplest and most basic way to test this equation is to use this equation to describe the physical behavior of bound electrons in hydrogen atoms, which will certainly reproduce the theoretical results of Bohr model. In addition, this equation must also explain the fine structure given by sommerfeld model.
Soon, Schrodinger deduced the wave equation of relativity through the theory of relativity in De Broglie's paper. He applied this equation to hydrogen atom and calculated the wave function of bound electrons. Because Schrodinger does not consider the spin of electrons, the fine structure formula derived from this equation does not conform to Sommerfeld model. He had to modify this equation, remove the relativistic part, and use the remaining non-relativistic equation to calculate the spectral lines of hydrogen atoms. It is very difficult to analyze this differential equation. With the help of friend mathematician Herman Weil, he copied the exact same answer as Bohr's model. Therefore, he decided not to publish the relativistic part for the time being, but only to write a paper on the non-relativistic wave equation and the spectral analysis results of hydrogen atoms. 1926, he officially published this paper.
This paper quickly caused a shock in the quantum academic community. Planck said, "He read the whole paper, just like a child who has been puzzled by a riddle for a long time and is eager to know the answer, and now he finally hears the answer." Einstein praised that this book was inspired by a real genius, like a spring. Einstein felt that Schrodinger made a decisive contribution. Because Schrodinger's wave mechanics involves familiar wave concepts and mathematics, rather than abstract and unfamiliar matrix algebra in matrix mechanics, quantum scholars are willing to start learning and applying wave mechanics. George Uhlenbeck, the discoverer of spin, exclaimed: "The Schrodinger equation has brought us great relief!" Wolfgang Pauli believes that this paper should be regarded as one of the most important works.
The Schrodinger equation given by Schrodinger can correctly describe the quantum behavior of wave function. At that time, physicists didn't know how to explain the wave function. Schrodinger tried to explain the absolute square of wave function by charge density, but he failed. 1926, born put forward the concept of probability amplitude, which successfully explained the physical meaning of wave function. However, Schrodinger and Einstein share the same view, and they do not agree with this statistical or probabilistic method and its accompanying discontinuous wave function collapse. Einstein thought that quantum mechanics was a statistical approximation of decisive theory. In the last year of Schrodinger's life, in a letter to Born, he made it clear that he did not accept the Copenhagen interpretation.