It is a second-order partial differential equation established by combining the concept of matter wave with wave equation, which can describe the movement of microscopic particles. Every microscopic system has its own Schrodinger equation. By solving the equation, we can get the specific form of wave function and the corresponding energy, so as to understand the properties of micro-system.
Schrodinger equation shows that in quantum mechanics, particles appear in a probabilistic way, which is uncertain and the failure can be ignored on the macro scale.