After reading Einstein's paper on quantum statistics, Schrodinger thought that the old quantum theory was not satisfactory, so he began to study the atomic structure with a brand-new point of view. Schrodinger published a series of four papers entitled "Quantization as an Eigenvalue Problem" in 1926 10, February, May and June in the German Journal of Physics, and the last one was sent to the magazine around June 22nd. These four papers establish a complete wave mechanics.
In his paper on June+10, 5438, he established and solved the stationary Schrodinger equation and energy level formula of hydrogen atom by using Hamiltonian-Jacobian equation and variational method of classical mechanics, and replaced the original Bohr-Sommerfeld quantization condition with eigenvalue, thus reducing the quantization problem to eigenvalue problem, which is a creative way for Schrodinger to establish wave mechanics. In February's paper, he established and solved the time-dependent Schrodinger equation, and expounded the significance of wave mechanics and wave function through the analogy between classical mechanics and geometric optics. The papers published in May and June introduced the time-independent Schrodinger perturbation theory and the time-related Schrodinger perturbation theory in detail.
Wave mechanics greatly developed De Broglie's thought and further explained the essence of wave-particle duality of microscopic objects. This theory has become a powerful tool for studying microscopic particles such as atoms and molecules, and laid a theoretical foundation for the interaction of basic particles. Schrodinger equation is a non-relativistic theory, because it is based on two assumptions: the production and annihilation of physical particles do not occur, and the speed of physical particles is much less than the speed of light.
Schrodinger and Dirac both won the 1933 Nobel Prize in Physics for their new atomic theory. British mathematician Wells solved Fermat's conjecture.
About 1630, the French mathematician Fermat (P? d？ Fermat) generalizes the eighth proposition in the second volume of Arithmetic written by Diophantine in ancient Greece, and obtains the following proposition: When n≥3, there is no positive integer solution to the indefinite equation xn+yn=zn. This is Fermat's conjecture.
After Zimmer's death, many mathematicians such as Leibniz and Euler (L? Euler), Legendre (a? m？ Legendre), Gauss, Cauchy, Dirichlet (P? g？ L Direchlet) and kummer (e? e？ Kummer) and others tried to prove this conjecture, but some of them only gave proof as special cases, and some even gave wrong proof.
No matter how difficult the problem is, it can't stop people from exploring. 1955, Japanese mathematicians Taniyama and Zhicun put forward the Taniyama-Zhicun conjecture. 1986, German mathematician Frey (G? Frey) found that if the Taniyama-Zhicun conjecture holds, so does the Fermat conjecture. In the same year, American mathematician Bei (K? Ribet) proved Searle (J? p？ Searle's "horizontal reduction conjecture" Therefore, to prove Fermat's conjecture, we only need to prove that the Taniyama-Zhicun conjecture is established. The above work paved the way for Wells to finally solve Fermat's conjecture.
Wells was born in Cambridge, England on April 1954+0 1. At the age of ten, he became interested in Fermat's conjecture, and the work of Frey and Ribe greatly inspired Wells. Later, Wells made a detailed plan and devoted himself to the study of Fermat's conjecture. 1On June 23, 993, Wells announced to the participants in a calm tone: "I proved Fermat's conjecture." However, Wells did not publish his paper immediately, but kept checking for mistakes. After nearly two years of revision and improvement, the full text of the paper was published in May 1995. At this point, this problem that has plagued the mathematics community for more than 300 years has been solved, and Wells won the Fields Special Contribution Award with 1998.