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 on 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.